Thursday, June 27, 2013
for quiz 8
Four forces of nature
Basics of stars - gravity vs. strong nuclear force
O B A F G K M - stellar types
H-R diagram
Main sequence (dwarf stars)
white dwarfs and giants/supergiants
Basics of stellar evolution
Basics of stars - gravity vs. strong nuclear force
O B A F G K M - stellar types
H-R diagram
Main sequence (dwarf stars)
white dwarfs and giants/supergiants
Basics of stellar evolution
Stars
There are 4 fundamental forces of nature:
Strong nuclear - this keeps protons close together
Weak nuclear a responsible for radioactive decay
Electromagnetism - light, electricity, magnetism, etc
Gravity - weakest of all, but furthest reaching
A star (Latin root stella-) is essentially a ball of gas powered by nuclear reactions, held together by gravity.
Stars may appear white, but their color is a conbination of many colors (and non visible e-m waves like uv).
Spectral types are listed in order of decreasing temperature:
O B A F G K M
with a temperature range from 60,000 K down to under 3500 K.
There are further subdivisions (C and S stars under M).
You can learn a lot about a star from where it lies on the Hertzsprung-Russel diagram.
The H-R diagram plots magnitude (brightness, from dim to bright) vs. temperature (high to low, usually as spectral type).
Hottest stars are on the left if the graph - they are normally brighter than cooler stars.
Most stars fall on along a diagonal band from upper left to lower right on the H-R diagram. We call this the Main Sequence, and the stars there are main sequence stars or dwarfs (which is a misleading term).
Stars above and to the right of the MS are giants (including supergiants).
Faint hit objects (white dwarfs) are below and to the left of the MS.
Strong nuclear - this keeps protons close together
Weak nuclear a responsible for radioactive decay
Electromagnetism - light, electricity, magnetism, etc
Gravity - weakest of all, but furthest reaching
A star (Latin root stella-) is essentially a ball of gas powered by nuclear reactions, held together by gravity.
Stars may appear white, but their color is a conbination of many colors (and non visible e-m waves like uv).
Spectral types are listed in order of decreasing temperature:
O B A F G K M
with a temperature range from 60,000 K down to under 3500 K.
There are further subdivisions (C and S stars under M).
You can learn a lot about a star from where it lies on the Hertzsprung-Russel diagram.
The H-R diagram plots magnitude (brightness, from dim to bright) vs. temperature (high to low, usually as spectral type).
Hottest stars are on the left if the graph - they are normally brighter than cooler stars.
Most stars fall on along a diagonal band from upper left to lower right on the H-R diagram. We call this the Main Sequence, and the stars there are main sequence stars or dwarfs (which is a misleading term).
Stars above and to the right of the MS are giants (including supergiants).
Faint hit objects (white dwarfs) are below and to the left of the MS.
The Sun
The Sun Photosphere - the part we see Sun’s composition is typical ~94% H ~5.9% He Radiation from the photosphere peaks in the middle of the visible spectrum We’ve evolved over time to have our eyesight most sensitive there About 10,000 km (~1.5% of solar radius) thick, directly above photosphere, is the jagged, spiky layer called the chromosphere (seen pinkish during an eclipse) Above this layer is the corona, extending tens of millions of kms into space - solar wind We’re bathed in this solar wind Photosphere Surface temp about 5800 K We can resolve details to about 700 km across Granulation at surface, but current telescope resolution isn’t quite enough to distinguish details Photosphere oscillates up and down, which tells us about interior (temperature, density, rate of rotation of interior) Chromosphere Look at sun through an H-filter to see this layer Temp is between7000 K and 15,000 K - higher than photosphere Composed of small spicules - jets of gas rising and falling, looking like blades of grass some 7000 km tall, 700 km across, lasting 5 to 15 minutes Corona Very irregular in shape - streamers away from sun Too faint to see, except during eclipses Temp near 2,000,000 K at lowest levels Emits mainly x-rays There are a few “cooler” holes - out of which solar flows to Earth Corona is not uniform Sunspots 11-year cycle (first noted in 1850) Dark center - umbra Surrounded by penumbra Regions of high magnetic field strength (1000’s of times stronger than that of Earth) Discovered by Galileo in 1610 by projection of solar image There was an instance between 1645 and 1715 where there were NO sunspots the Maunder minimum - activity is less regular than imght be thought, though the evidence is a bit sketchy; perhaps Earth’s climate affected observing Every 11 years, Sun’s north and south magnetic poles reverse
Hertzsprung-Russell Diagram
One of the most useful tools for identifying star types in astronomy is the H-R Diagram. This idea, independently conceived in 1910 by Ejnar Hertzsprung and Henry Russell, is a graphical representation of intrinsic brightness as a function of temperature. It is largely based on this diagram that stars are classified.
There are a few variations of the H-R diagram:
• Absolute visual magnitude (Mv) vs. Spectral Type
• Absolute visual magnitude vs. Temperature
• Luminosity of star (sometimes given as relative to Sun’s luminosity) vs. Spectral Type
• Absolute visual magnitude vs. Color Index (B - V)
Other variations exist as well. The purpose and effect of each diagram is the same, however. Points plotted fall in limited regions on the graph, rather than in a wide distribution.
The Spectral Types are (in order of decreasing temperature):
O, B, A, F, G, K, M
Further, each of these can be subdivided into 10 categories, 0-9, though most of our stars today will be in the 0-5 range. Your graph will resemble the graph noted on the board in class.
There is a broad roughly diagonal band running from upper left to lower right. This is referred to as the Main Sequence. Most stars spend the bulk of their lives along the Main Sequence
Blue moon
From Neil deGrasse Tyson (via his facebook feed):
The average time the Moon takes to complete a cycle of phases is 29.5 days. So all months but February can host a second full Moon, if the timing is right. We call these "Blue Moons" and we get one on Friday, August 31. Chances of a full Moon on the first of a month is about 1 in 30, so you'd expect a Blue Moon every 30 months or so -- about once every 2.5 years. Not rare. So when the cosmically literate want to reference something that's uncommon, they **never** say "Once in a Blue Moon". -NDTyson
Activity 4 (homework) for the FINAL class
Research a little about SETI and the Drake Equation. Prepare a short summary about the key findings, etc. Short = 1 page or so.
If you would rather investigate other ways to search for extraterrestrial life, feel free to do that. Again, a 1-page summary is what I would like.
If you would rather investigate other ways to search for extraterrestrial life, feel free to do that. Again, a 1-page summary is what I would like.
Meteor Showers this year, FYI
http://earthsky.org/astronomy-essentials/earthskys-meteor-shower-guide
Alternative lab 3 - Winter Observing
This is similar to the summer observing lab. Go back in time a few months ago:
http://skymaps.com/downloads.html
for the map
http://skymaps.com/articles/index.html
for the calendar
Print out a star chart from January and answer these questions based on that. Enjoy! And be sure to try this once the winter comes. Observing is much better then, despite the cold.
1. List the asterisms visible.
2. List the constellations visible.
3. Describe how to find north.
4. What planets, if any, are visible?
5. What is the winter triangle? Discuss.
6. What is the winter hexagon? Discuss.
7. Answer these questions based on Orion:
a. What are the two brightest stars. Give the names (and colors).
b. What are the names of the 3 belt stars.
c. What type of object is located just "below the belt"?
d. Following the belt stars, find the two bright stars on either side that are nearest in line.
e. Give some information about the mythology of Orion.
8. What is directly overhead (at zenith)?
9. Locate the Pleiades and Hyades clusters. How would you find them in the sky?
10. How would you locate the Andromeda galaxy (M31)?
11. What interesting things are happening or visible during this month?
12. How does the winter sky differ from the summer sky? Discuss.
http://skymaps.com/downloads.html
for the map
http://skymaps.com/articles/index.html
for the calendar
Print out a star chart from January and answer these questions based on that. Enjoy! And be sure to try this once the winter comes. Observing is much better then, despite the cold.
1. List the asterisms visible.
2. List the constellations visible.
3. Describe how to find north.
4. What planets, if any, are visible?
5. What is the winter triangle? Discuss.
6. What is the winter hexagon? Discuss.
7. Answer these questions based on Orion:
a. What are the two brightest stars. Give the names (and colors).
b. What are the names of the 3 belt stars.
c. What type of object is located just "below the belt"?
d. Following the belt stars, find the two bright stars on either side that are nearest in line.
e. Give some information about the mythology of Orion.
8. What is directly overhead (at zenith)?
9. Locate the Pleiades and Hyades clusters. How would you find them in the sky?
10. How would you locate the Andromeda galaxy (M31)?
11. What interesting things are happening or visible during this month?
12. How does the winter sky differ from the summer sky? Discuss.
More videos, if you have time this summer
The Pale Blue Dot video (narrated by Carl Sagan)
Neil deGrasse
Tyson with Colbert
And if you ever
have an hour to spare, Richard Feynman (a hero of mine):
For fun
Related to our discuss last class
Regarding, "how did life originate?"
A decent 5-minute clip that dramatizes evolution. It's a bit simplistic, and it doesn't stress that evolution is more like a tree with many branches. Still, interesting and pretty well done:
https://www.youtube.com/watch?v=QH27ug9YMVY
Also:
https://www.youtube.com/watch?v=s-nLJI2BZIM
http://en.wikipedia.org/wiki/Abiogenesis
It's a long read, but it is a pretty complex history.
If you have an hour or three to kill, here are good documentaries:
https://www.youtube.com/watch?v=zy64KR6vYU4
https://www.youtube.com/watch?v=K7tQIB4UdiY
https://www.youtube.com/watch?v=3o5QlNrUBGw
More information about what makes humans special:
https://www.youtube.com/watch?v=gnSf7pAjw38
https://www.youtube.com/watch?v=w_wSECz4O88
A decent 5-minute clip that dramatizes evolution. It's a bit simplistic, and it doesn't stress that evolution is more like a tree with many branches. Still, interesting and pretty well done:
https://www.youtube.com/watch?v=QH27ug9YMVY
Also:
https://www.youtube.com/watch?v=s-nLJI2BZIM
http://en.wikipedia.org/wiki/Abiogenesis
It's a long read, but it is a pretty complex history.
If you have an hour or three to kill, here are good documentaries:
https://www.youtube.com/watch?v=zy64KR6vYU4
https://www.youtube.com/watch?v=K7tQIB4UdiY
https://www.youtube.com/watch?v=3o5QlNrUBGw
More information about what makes humans special:
https://www.youtube.com/watch?v=gnSf7pAjw38
https://www.youtube.com/watch?v=w_wSECz4O88
Wednesday, June 26, 2013
Tuesday, June 25, 2013
For quiz 7
Topics for next quiz:
apparent magnitude - remember the factor of 2.5 between each magnitude, and also that the scale goes from negative numbers (brightest) to positive numbers (dimmest)
absolute magnitude - a measure of the star's ACTUAL brightness (which is determined by the radius and temperature
Know the difference between apparent magnitude (m) and absolute magnitude (M).
Doppler effect - know what it is and how it works. Review the applets if necessary.
Know your blue shift from red shift.
Basics of formation of solar system.
Formation of Moon (current theory). FYI:
http://www.youtube.com/watch?v=Fwl_JBQtH9o
http://www.youtube.com/watch?v=ibV4MdN5wo0
(If you're feeling crazy, and have a smartphone, look for the Exoplanet app. You won't find it as cool as I do, but still.... it's neat to see how many extra-solar planets there are!)
apparent magnitude - remember the factor of 2.5 between each magnitude, and also that the scale goes from negative numbers (brightest) to positive numbers (dimmest)
absolute magnitude - a measure of the star's ACTUAL brightness (which is determined by the radius and temperature
Know the difference between apparent magnitude (m) and absolute magnitude (M).
Doppler effect - know what it is and how it works. Review the applets if necessary.
Know your blue shift from red shift.
Basics of formation of solar system.
Formation of Moon (current theory). FYI:
http://www.youtube.com/watch?v=Fwl_JBQtH9o
http://www.youtube.com/watch?v=ibV4MdN5wo0
(If you're feeling crazy, and have a smartphone, look for the Exoplanet app. You won't find it as cool as I do, but still.... it's neat to see how many extra-solar planets there are!)
Full Moon Names
http://www.farmersalmanac.com/full-moon-names/
Full Moon Names and Their Meanings
Full Moon names date back to Native Americans, of what is now the
northern and eastern United States. The tribes kept track of the seasons
by giving distinctive names to each recurring full Moon. Their names
were applied to the entire month in which each occurred. There was some
variation in the Moon names, but in general, the same ones were current
throughout the Algonquin tribes from New England to Lake Superior.
European settlers followed that custom and created some of their own
names. Since the lunar month is only 29 days long on the average, the
full Moon dates shift from year to year. Here is the Farmers Almanac’s
list of the full Moon names.
• Full Wolf Moon – January Amid the cold and deep snows of midwinter, the wolf packs howled hungrily outside Indian villages. Thus, the name for January’s full Moon. Sometimes it was also referred to as the Old Moon, or the Moon After Yule. Some called it the Full Snow Moon, but most tribes applied that name to the next Moon.
• Full Snow Moon – February Since the heaviest snow usually falls during this month, native tribes of the north and east most often called February’s full Moon the Full Snow Moon. Some tribes also referred to this Moon as the Full Hunger Moon, since harsh weather conditions in their areas made hunting very difficult.
• Full Worm Moon – March As the temperature begins to warm and the ground begins to thaw, earthworm casts appear, heralding the return of the robins. The more northern tribes knew this Moon as the Full Crow Moon, when the cawing of crows signaled the end of winter; or the Full Crust Moon, because the snow cover becomes crusted from thawing by day and freezing at night. The Full Sap Moon, marking the time of tapping maple trees, is another variation. To the settlers, it was also known as the Lenten Moon, and was considered to be the last full Moon of winter.
• Full Pink Moon – April This name came from the herb moss pink, or wild ground phlox, which is one of the earliest widespread flowers of the spring. Other names for this month’s celestial body include the Full Sprouting Grass Moon, the Egg Moon, and among coastal tribes the Full Fish Moon, because this was the time that the shad swam upstream to spawn.
• Full Flower Moon – May In most areas, flowers are abundant everywhere during this time. Thus, the name of this Moon. Other names include the Full Corn Planting Moon, or the Milk Moon.
• Full Strawberry Moon – June This name was universal to every Algonquin tribe. However, in Europe they called it the Rose Moon. Also because the relatively short season for harvesting strawberries comes each year during the month of June . . . so the full Moon that occurs during that month was christened for the strawberry!
• The Full Buck Moon – July July is normally the month when the new antlers of buck deer push out of their foreheads in coatings of velvety fur. It was also often called the Full Thunder Moon, for the reason that thunderstorms are most frequent during this time. Another name for this month’s Moon was the Full Hay Moon.
• Full Sturgeon Moon – August The fishing tribes are given credit for the naming of this Moon, since sturgeon, a large fish of the Great Lakes and other major bodies of water, were most readily caught during this month. A few tribes knew it as the Full Red Moon because, as the Moon rises, it appears reddish through any sultry haze. It was also called the Green Corn Moon or Grain Moon.
• Full Corn Moon or Full Harvest Moon – September This full moon’s name is attributed to Native Americans because it marked when corn was supposed to be harvested. Most often, the September full moon is actually the Harvest Moon, which is the full Moon that occurs closest to the autumn equinox. In two years out of three, the Harvest Moon comes in September, but in some years it occurs in October. At the peak of harvest, farmers can work late into the night by the light of this Moon. Usually the full Moon rises an average of 50 minutes later each night, but for the few nights around the Harvest Moon, the Moon seems to rise at nearly the same time each night: just 25 to 30 minutes later across the U.S., and only 10 to 20 minutes later for much of Canada and Europe. Corn, pumpkins, squash, beans, and wild rice the chief Indian staples are now ready for gathering.
• Full Hunter’s Moon or Full Harvest Moon – October This full Moon is often referred to as the Full Hunter’s Moon, Blood Moon, or Sanguine Moon. Many moons ago, Native Americans named this bright moon for obvious reasons. The leaves are falling from trees, the deer are fattened, and it’s time to begin storing up meat for the long winter ahead. Because the fields were traditionally reaped in late September or early October, hunters could easily see fox and other animals that come out to glean from the fallen grains. Probably because of the threat of winter looming close, the Hunter’s Moon is generally accorded with special honor, historically serving as an important feast day in both Western Europe and among many Native American tribes.
• Full Beaver Moon – November This was the time to set beaver traps before the swamps froze, to ensure a supply of warm winter furs. Another interpretation suggests that the name Full Beaver Moon comes from the fact that the beavers are now actively preparing for winter. It is sometimes also referred to as the Frosty Moon.
• The Full Cold Moon; or the Full Long Nights Moon – December During this month the winter cold fastens its grip, and nights are at their longest and darkest. It is also sometimes called the Moon before Yule. The term Long Night Moon is a doubly appropriate name because the midwinter night is indeed long, and because the Moon is above the horizon for a long time. The midwinter full Moon has a high trajectory across the sky because it is opposite a low Sun.
• Full Wolf Moon – January Amid the cold and deep snows of midwinter, the wolf packs howled hungrily outside Indian villages. Thus, the name for January’s full Moon. Sometimes it was also referred to as the Old Moon, or the Moon After Yule. Some called it the Full Snow Moon, but most tribes applied that name to the next Moon.
• Full Snow Moon – February Since the heaviest snow usually falls during this month, native tribes of the north and east most often called February’s full Moon the Full Snow Moon. Some tribes also referred to this Moon as the Full Hunger Moon, since harsh weather conditions in their areas made hunting very difficult.
• Full Worm Moon – March As the temperature begins to warm and the ground begins to thaw, earthworm casts appear, heralding the return of the robins. The more northern tribes knew this Moon as the Full Crow Moon, when the cawing of crows signaled the end of winter; or the Full Crust Moon, because the snow cover becomes crusted from thawing by day and freezing at night. The Full Sap Moon, marking the time of tapping maple trees, is another variation. To the settlers, it was also known as the Lenten Moon, and was considered to be the last full Moon of winter.
• Full Pink Moon – April This name came from the herb moss pink, or wild ground phlox, which is one of the earliest widespread flowers of the spring. Other names for this month’s celestial body include the Full Sprouting Grass Moon, the Egg Moon, and among coastal tribes the Full Fish Moon, because this was the time that the shad swam upstream to spawn.
• Full Flower Moon – May In most areas, flowers are abundant everywhere during this time. Thus, the name of this Moon. Other names include the Full Corn Planting Moon, or the Milk Moon.
• Full Strawberry Moon – June This name was universal to every Algonquin tribe. However, in Europe they called it the Rose Moon. Also because the relatively short season for harvesting strawberries comes each year during the month of June . . . so the full Moon that occurs during that month was christened for the strawberry!
• The Full Buck Moon – July July is normally the month when the new antlers of buck deer push out of their foreheads in coatings of velvety fur. It was also often called the Full Thunder Moon, for the reason that thunderstorms are most frequent during this time. Another name for this month’s Moon was the Full Hay Moon.
• Full Sturgeon Moon – August The fishing tribes are given credit for the naming of this Moon, since sturgeon, a large fish of the Great Lakes and other major bodies of water, were most readily caught during this month. A few tribes knew it as the Full Red Moon because, as the Moon rises, it appears reddish through any sultry haze. It was also called the Green Corn Moon or Grain Moon.
• Full Corn Moon or Full Harvest Moon – September This full moon’s name is attributed to Native Americans because it marked when corn was supposed to be harvested. Most often, the September full moon is actually the Harvest Moon, which is the full Moon that occurs closest to the autumn equinox. In two years out of three, the Harvest Moon comes in September, but in some years it occurs in October. At the peak of harvest, farmers can work late into the night by the light of this Moon. Usually the full Moon rises an average of 50 minutes later each night, but for the few nights around the Harvest Moon, the Moon seems to rise at nearly the same time each night: just 25 to 30 minutes later across the U.S., and only 10 to 20 minutes later for much of Canada and Europe. Corn, pumpkins, squash, beans, and wild rice the chief Indian staples are now ready for gathering.
• Full Hunter’s Moon or Full Harvest Moon – October This full Moon is often referred to as the Full Hunter’s Moon, Blood Moon, or Sanguine Moon. Many moons ago, Native Americans named this bright moon for obvious reasons. The leaves are falling from trees, the deer are fattened, and it’s time to begin storing up meat for the long winter ahead. Because the fields were traditionally reaped in late September or early October, hunters could easily see fox and other animals that come out to glean from the fallen grains. Probably because of the threat of winter looming close, the Hunter’s Moon is generally accorded with special honor, historically serving as an important feast day in both Western Europe and among many Native American tribes.
• Full Beaver Moon – November This was the time to set beaver traps before the swamps froze, to ensure a supply of warm winter furs. Another interpretation suggests that the name Full Beaver Moon comes from the fact that the beavers are now actively preparing for winter. It is sometimes also referred to as the Frosty Moon.
• The Full Cold Moon; or the Full Long Nights Moon – December During this month the winter cold fastens its grip, and nights are at their longest and darkest. It is also sometimes called the Moon before Yule. The term Long Night Moon is a doubly appropriate name because the midwinter night is indeed long, and because the Moon is above the horizon for a long time. The midwinter full Moon has a high trajectory across the sky because it is opposite a low Sun.
Moon
THE MOON
Highlands - heavy cratered
Mare (maria, pl.) - smooth
Mass of moon = 1/81 Earth mass
gravity of moon - 1/6 Earth gravity
Diameter of moon - 1/4 Earth diameter
Mountain ranges (formed by debris) and valleys
Ridges and high crater rims
Moon rotates on axis at same rate as its rotation
about the Earth
Synodic Period (about 29.5 days for moon)
As a result, same face is always toward Earth
Most locations in sunlight for 15 days (temp = 130 C)
Also in darkness for 15 days (-110 C)
July 20, 1969 - Aldrin and Armstrong walk on moon
(Apollo 11) while Collins orbits
Six moon missions total (Apollo program)
Lunar Surface:
igneous rocks - formed by lava cooling
few sedimentary rocks (settling)
Thick crust (12% of total volume)
in maria, rocks are mainly basalts
in highlands, anorthosites (rare on earth)
some rocks are breccias (mixtures, welded together)
soil - bits of dust and fragments, small glassy
globules
NO WATER - no life.
Dating of moon done by:
Radioactive dating of material brought back
crater dating (which areas are most heavily cratered)
Craters with rays have formed more recently (they
formed over other areas)
General picture:
Moon formed about 4.6 billion years ago
top 100 km or so was molten for about 200 million
years after
From 4.2 to 3.9 billion years ago:
Heavy bombardment by planetesimals
Moon heated up from radioactive elements inside -
volcanism began
lava flowed onto surface
By 3.1 billion years ago, era of volcanism ends
active lunar history ends (here ends similarity with
Earth)
No tectonics or erosion
Interior
crust: light material, with silica-rich mantle
metallic (iron) core
seismically quiet compared to earth (not totally
sure)
minor magnetic field, frozen into lunar rocks
(possibly left over from old molten core)
slow heat flow from core to surface (1/3 of earth’s)
Origin of moon theories
1. Fission - separated from earth
2. Capture - captured by earth
3. Condensation - formed near and simultaneously with
earth
1 - 3 === > probably not
4. interaction of earth with planetesimals which
formed moon
5. ejection of ring when earth was hit by
planetesimal
Highlands - heavy cratered
Mare (maria, pl.) - smooth
Mass of moon = 1/81 Earth mass
gravity of moon - 1/6 Earth gravity
Diameter of moon - 1/4 Earth diameter
Mountain ranges (formed by debris) and valleys
Ridges and high crater rims
Moon rotates on axis at same rate as its rotation
about the Earth
Synodic Period (about 29.5 days for moon)
As a result, same face is always toward Earth
Most locations in sunlight for 15 days (temp = 130 C)
Also in darkness for 15 days (-110 C)
July 20, 1969 - Aldrin and Armstrong walk on moon
(Apollo 11) while Collins orbits
Six moon missions total (Apollo program)
Lunar Surface:
igneous rocks - formed by lava cooling
few sedimentary rocks (settling)
Thick crust (12% of total volume)
in maria, rocks are mainly basalts
in highlands, anorthosites (rare on earth)
some rocks are breccias (mixtures, welded together)
soil - bits of dust and fragments, small glassy
globules
NO WATER - no life.
Dating of moon done by:
Radioactive dating of material brought back
crater dating (which areas are most heavily cratered)
Craters with rays have formed more recently (they
formed over other areas)
General picture:
Moon formed about 4.6 billion years ago
top 100 km or so was molten for about 200 million
years after
From 4.2 to 3.9 billion years ago:
Heavy bombardment by planetesimals
Moon heated up from radioactive elements inside -
volcanism began
lava flowed onto surface
By 3.1 billion years ago, era of volcanism ends
active lunar history ends (here ends similarity with
Earth)
No tectonics or erosion
Interior
crust: light material, with silica-rich mantle
metallic (iron) core
seismically quiet compared to earth (not totally
sure)
minor magnetic field, frozen into lunar rocks
(possibly left over from old molten core)
slow heat flow from core to surface (1/3 of earth’s)
Origin of moon theories
1. Fission - separated from earth
2. Capture - captured by earth
3. Condensation - formed near and simultaneously with
earth
1 - 3 === > probably not
4. interaction of earth with planetesimals which
formed moon
5. ejection of ring when earth was hit by
planetesimal
Formation of the Solar System
Formation of Solar System
~ 4.6 billion years ago huge cloud of gas and dust
started collapsing gravitationally
• As it collapsed it spun faster (conservation of
angular momentum)
• No (or little) spin in the perpendicular plane
• Local clusters of dust and gas condensed - protosun
formed first
• As material cooled, it condensed but never stopped
rotating (rotates still since there’s nothing to stop
it)
• Cores probably formed first, then attracted
neighboring materials to form: planetesimal,
protoplanet
• Probably not a unique system - there is increasing
evidence for the existence of many other planetary
systems
• Still an evolving theory
• All planets revoluve around the sun in the same
direction, but 3 have different directions of rotation
(relative to the rest and to the direction of solar
system motion) - Uranus, Venus, Pluto
The Terrestrial Planets: Mercury, Venus, Earth, and
Mars
Relative Characteristics:
Planet Distance Period Radius Mass
Mercury 0.4 0.24 0.38 0.055
Venus 0.7 0.62 0.95 0.82
Earth 1 1 1 1
Mars 1.5 1.88 0.53 0.11
The Jovian Planets (gas giants)
Jupiter 5.2 11.9 11.2 318
Saturn 9.5 29.5 9.3 95
Uranus 19 84 4.0 14.6
Neptune 30 165 3.9 17.2
~ 4.6 billion years ago huge cloud of gas and dust
started collapsing gravitationally
• As it collapsed it spun faster (conservation of
angular momentum)
• No (or little) spin in the perpendicular plane
• Local clusters of dust and gas condensed - protosun
formed first
• As material cooled, it condensed but never stopped
rotating (rotates still since there’s nothing to stop
it)
• Cores probably formed first, then attracted
neighboring materials to form: planetesimal,
protoplanet
• Probably not a unique system - there is increasing
evidence for the existence of many other planetary
systems
• Still an evolving theory
• All planets revoluve around the sun in the same
direction, but 3 have different directions of rotation
(relative to the rest and to the direction of solar
system motion) - Uranus, Venus, Pluto
The Terrestrial Planets: Mercury, Venus, Earth, and
Mars
Relative Characteristics:
Planet Distance Period Radius Mass
Mercury 0.4 0.24 0.38 0.055
Venus 0.7 0.62 0.95 0.82
Earth 1 1 1 1
Mars 1.5 1.88 0.53 0.11
The Jovian Planets (gas giants)
Jupiter 5.2 11.9 11.2 318
Saturn 9.5 29.5 9.3 95
Uranus 19 84 4.0 14.6
Neptune 30 165 3.9 17.2
Thursday, June 20, 2013
The Analemma
http://en.wikipedia.org/wiki/Analemma
1. The Earth is tilted on its axis 23.5° in relation to the plane of its orbit around the sun.
2. The Earth does not orbit the sun in a circle, but in an ellipse.
It is simply the sum of these two effects that causes the analemma - an apparent path of the Sun, looking at it at the same time every day (or every few days).
Do a Google image search for analemma and you'll see how the inclination of the analemma depends on latitude.
http://www.perseus.gr/Astro-Solar-Analemma.htm
1. The Earth is tilted on its axis 23.5° in relation to the plane of its orbit around the sun.
2. The Earth does not orbit the sun in a circle, but in an ellipse.
It is simply the sum of these two effects that causes the analemma - an apparent path of the Sun, looking at it at the same time every day (or every few days).
Do a Google image search for analemma and you'll see how the inclination of the analemma depends on latitude.
http://www.perseus.gr/Astro-Solar-Analemma.htm
Phases of the Moon
http://astro.unl.edu/naap/lps/animations/lps.html
http://www.astro.wisc.edu/~dolan/java/MoonPhase.html
http://www.moonconnection.com/moon_phases.phtml
http://www.astro.wisc.edu/~dolan/java/MoonPhase.html
http://www.moonconnection.com/moon_phases.phtml
The Doppler Effect
See this simple, but effective applet:
http://lectureonline.cl.msu.edu/~mmp/applist/doppler/d.htm
In this simulation, v/vs is the ratio of your speed to the speed of sound; e.g., 0.5 is you, or the blue dot, traveling at half the speed of sound. Note how the waves experienced on one side "pile up" (giving an observer a greater detected frequency, or BLUE SHIFT); on the other side, the waves are "stretched apart" (giving an observer a lower detected frequency, or RED SHIFT).
Play with this for a bit, though it's a little less obvious:
http://falstad.com/ripple/
In astronomy, the red shift is very important historically: Edwin Hubble found that light from distant galaxies (as measured in their spectra) was red shifted, meaning that distant galaxies were moving away from us (everywhere we looked). The conclusion was obvious (and startling): The universe is expanding. Last year, local astrophysicist Adam Riess discovered that the rate of expansion was accelerating.
http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/
It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you move away from a detector move away from a sound-emitter, you'll detect a lower frequency.
Mind you, these Doppler effects only happen WHILE there is relative motion between source and detector (you).
And of course, they also work for light. That's why we care about them. In fact, the terms red shift and blue shift refer mainly to light (or other electromagnetic) phenomena.
http://lectureonline.cl.msu.edu/~mmp/applist/doppler/d.htm
In this simulation, v/vs is the ratio of your speed to the speed of sound; e.g., 0.5 is you, or the blue dot, traveling at half the speed of sound. Note how the waves experienced on one side "pile up" (giving an observer a greater detected frequency, or BLUE SHIFT); on the other side, the waves are "stretched apart" (giving an observer a lower detected frequency, or RED SHIFT).
Play with this for a bit, though it's a little less obvious:
http://falstad.com/ripple/
In astronomy, the red shift is very important historically: Edwin Hubble found that light from distant galaxies (as measured in their spectra) was red shifted, meaning that distant galaxies were moving away from us (everywhere we looked). The conclusion was obvious (and startling): The universe is expanding. Last year, local astrophysicist Adam Riess discovered that the rate of expansion was accelerating.
http://www.nobelprize.org/nobel_prizes/physics/laureates/2011/
It's worth noting that the effect also works in reverse. If you (the detector) move toward a sound-emitter, you'll detect a higher frequency. If you move away from a detector move away from a sound-emitter, you'll detect a lower frequency.
Mind you, these Doppler effects only happen WHILE there is relative motion between source and detector (you).
And of course, they also work for light. That's why we care about them. In fact, the terms red shift and blue shift refer mainly to light (or other electromagnetic) phenomena.
Alternate lab #2 - Planet quest
Planet "lab"
A Tour of the Planets
Please determine many interesting tidbits of trivia about our solar neighbors. You may like the following website:
http://nineplanets.org/
Please answer the following questions, based on your reading and web discovery. Some questions might have several answers, while the answer to others might be "none of them."
Please determine many interesting tidbits of trivia about our solar neighbors. You may like the following website:
http://nineplanets.org/
Please answer the following questions, based on your reading and web discovery. Some questions might have several answers, while the answer to others might be "none of them."
Which planet(s):
1. Rotates backwards?
2. Revolves backwards?
3. Rotates nearly on its side?
4. Have more than 10 moons?
5. Have only one moon?
6. Has an orbit with the greatest inclination to the ecliptic?
7. Is the furthest planet known to the ancients?
8. Has a largely methane atmosphere?
9. Has a nondescript, pale greenish color?
10. Has a blemish known as the great dark spot?
11. Has a fine iron oxide regolith?
12. Is most similar to Earth in its surface gravity?
13. Has the greatest mass?
14. Has the smallest diameter?
15. Have been visited by humans?
16. Has the strongest magnetic field?
17. Has rings?
18. Has sulfuric acid clouds?
19. Has the tallest mountain in the Solar System (and what is it)?
20. Has a day longer than its year?
21. Has been landed on most recently by spacecraft?
22. Experiences global dust storms?
23. Has a moon that rotates retrograde (and what is it)?
24. May be an escaped Kuiper object?
25. Was once thought to be a failed star?
26. Is heavily cratered?
27. Has moons which are likely candidates for life?
28. Was hit by a large comet in the last several years?
29. Is most oblate?
30. Has a central pressure 100 million times Earth's atmospheric pressure?
Now for the minor bodies.
1. Which body is an asteroid with its own orbiting asteroid?
2. Which moon has erupting volcanoes?
3. Which body is the largest asteroid?
4. Approximately how many known asteroids are there?
5. Approximately how many known Kuiper objects are there? What is the Kuiper belt?
6. How large is the Oort Cloud? What is the Oort Cloud?
7. Which moon was the first discovered after the Galilean satellites?
1. Rotates backwards?
2. Revolves backwards?
3. Rotates nearly on its side?
4. Have more than 10 moons?
5. Have only one moon?
6. Has an orbit with the greatest inclination to the ecliptic?
7. Is the furthest planet known to the ancients?
8. Has a largely methane atmosphere?
9. Has a nondescript, pale greenish color?
10. Has a blemish known as the great dark spot?
11. Has a fine iron oxide regolith?
12. Is most similar to Earth in its surface gravity?
13. Has the greatest mass?
14. Has the smallest diameter?
15. Have been visited by humans?
16. Has the strongest magnetic field?
17. Has rings?
18. Has sulfuric acid clouds?
19. Has the tallest mountain in the Solar System (and what is it)?
20. Has a day longer than its year?
21. Has been landed on most recently by spacecraft?
22. Experiences global dust storms?
23. Has a moon that rotates retrograde (and what is it)?
24. May be an escaped Kuiper object?
25. Was once thought to be a failed star?
26. Is heavily cratered?
27. Has moons which are likely candidates for life?
28. Was hit by a large comet in the last several years?
29. Is most oblate?
30. Has a central pressure 100 million times Earth's atmospheric pressure?
Now for the minor bodies.
1. Which body is an asteroid with its own orbiting asteroid?
2. Which moon has erupting volcanoes?
3. Which body is the largest asteroid?
4. Approximately how many known asteroids are there?
5. Approximately how many known Kuiper objects are there? What is the Kuiper belt?
6. How large is the Oort Cloud? What is the Oort Cloud?
7. Which moon was the first discovered after the Galilean satellites?
8. How many "extrasolar" planets are there? Which was the first discovered?
9. What is the status of Pluto and why was is "demoted" from planet status?
Additional - list anything you found interesting in your hunt. Or multiple things.
Tuesday, June 18, 2013
For next class
Quiz topics:
1. electromagnetic spectrum
2. the connection between speed, frequency and wavelength
3. the parts of a wave
4. the basics of how a lens works
5. the meaning of "spectrum" and what you viewed when looking through the diffraction glasses at the gas tubes
Things to consider for your brief planet presentation:
1. Origin of name
2. Comparison to Earth (mass, diameter, gravitation)
3. Does it have moons? Is there something interesting about its moons?
4. Period/time for one orbit
5. Distance (a) from Sun
6. Atmosphere?
7. What is the primary make-up of the planet?
8. Interesting features that can be seen on the planet
9. What you find particularly interesting or compelling about the planet
10. Anything really strange about your planet?
Please email me your notes before class. I can provide images and will post your notes to the blog.
1. electromagnetic spectrum
2. the connection between speed, frequency and wavelength
3. the parts of a wave
4. the basics of how a lens works
5. the meaning of "spectrum" and what you viewed when looking through the diffraction glasses at the gas tubes
Things to consider for your brief planet presentation:
1. Origin of name
2. Comparison to Earth (mass, diameter, gravitation)
3. Does it have moons? Is there something interesting about its moons?
4. Period/time for one orbit
5. Distance (a) from Sun
6. Atmosphere?
7. What is the primary make-up of the planet?
8. Interesting features that can be seen on the planet
9. What you find particularly interesting or compelling about the planet
10. Anything really strange about your planet?
Please email me your notes before class. I can provide images and will post your notes to the blog.
Wave notes
NOTES - THERE ARE 3 COMPLETE WAVES IN THE IMAGE ABOVE.
Frequency (f) - number of waves per second (in hertz, Hz)
Wavelength (l - this should really be lambda, the Greek symbol) - the length of one wave. It can also be thought of as the distance between 2 crests, 2 troughs or the distance from the start to finish of ONE wave.
Speed (v) - literally (in m/s), how fast one wave is traveling (relative to some background)
These 3 variables are related by this equation:
v = f l
That is, speed equals frequency times wavelength. With light waves, the speed is constant - it's the speed of light in a vacuum (3 x 10^8 m/s, or 186,000 miles/second).
Since the speed is constant, as the wavelength goes UP, the frequency goes DOWN. Or the other way around, if the frequency goes UP, the wavelength goes DOWN.
Lenses and mirrors, in pictures
Concave mirror - Light hits curved (parabolic) surface and "real" image forms.
Below, light passes through convex lenses and "real" image forms.
Angular Measurement
Angular Measurement
Consider the following convention which has been with us since the
rise of Babylonian mathematics:
There are 360 degrees per circle.
Each degree can be further divided into 60 minutes (60'), each called
an arcminute.
Each arcminute can be divided into 60 seconds (60"), each called an arcsecond.
Therefore, there are 3600 arcseconds in one degree.
Some rough approximations:
A fist extended at arm's length subtends an angle of approx. 10º.
A thumb extended at arm's length subtends an angle of approx. 2º.
The Moon (and Sun) subtend an angle of approx. 0.5º.
Human eye resolution (the ability to distinguish between 2 adjacent
objects) is limited to about 1 arcminute – roughly the diameter of a
dime at 60-m. Actually, given the size of our retina, we're limited
to a resolution of roughly 3'
So, to achieve better resolution, we need more aperture (ie., telescopes).
The Earth's atmosphere limits detail resolution to objects bigger than
0.5", the diameter of a dime at 7-km, or a human hair 2 football
fields away. This is usually reduced to 1" due to atmospheric
turbulence.
The parsec (pc)
definite as one parsec – that is, it has a parallax of one arcsec.
For example, if a star has a parallax angle (d) of 0.5 arcsec, it is
1/0.5 parsecs (or 2 parsecs) away.
The parsec (pc) is roughly 3.26 light years.
Distance (in pc) = 1 / d
where d is in seconds of arc.
Measuring star distances can be done by measuring their angle of
parallax – typically done over a 6-month period, seeing how the star's
position changes with respect to background stars in 6 months, during
which time the Earth has moved across its ellipse.
Unfortunately, this is limited to nearby stars, some 10,000. Consider
this: Proxima Centauri (nearest star) has a parallax angle of 0.75" –
a dime at 5-km. So, you need to repeat measurements over several
years for accuracy.
This works for stars up to about 300 LY away, less than 1% the
diameter of our galaxy!
[If the MW galaxy were reduced to 130 km (80 mi) in diameter, the
Solar System would be a mere 2 mm (0.08 inches) in width.]
Apparent magnitude (m) scale
bright or small.
Ptolemy classified things into numbers: 1-6, with 1 being brightest.
The brightest (1st magnitude) stars were 100 times brighter than the
faintest (6th magnitude). This convention remains standard to this
day. Still, this was very qualitative.
In the 19th century, with the advent of photographic means of
recording stars onto plates, a more sophisticated system was adopted.
It held to the original ideas of Ptolemy
A difference of 5 magnitudes (ie., from 1 to 6) is equivalent to a
factor of exactly 100 times. IN other words, 1st magnitude is 100x
brighter than 6th magnitude. Or, 6th magnitude is 1/100th as bright
as 1st mag.
This works well, except several bodies are brighter than (the
traditional) 1st mag.
So….. we have 0th magnitude and negative magnitudes for really bright objects.
Examples:
Sirius (brightest star): -1.5
Sun: -26.8
Moon: -12.6
Venus: -4.4
Canopus (2nd brightest star): -0.7
Faintest stars visible with eye: +6
Faintest stars visible from Earth: +24
Faintest stars visible from Hubble: +28
The magnitude factor is the 5th root of 100, which equals roughly
2.512 (about 2.5).
Keep in mind that this is APPARENT magnitude, which depends on
distance, actual star luminosity and interstellar matter.
Here's a problem: What is the brightness difference between two
objects of magnitudes -1 and 6?
Since they are 7 magnitudes apart, the distance is 2.5 to the 7th power, or 600.
For the math buffs: the formula for apparent magnitude comparison:
m1 – m2 = 2.5 log (I2 / I1)
The m's are magnitudes and the I's are intensities – the ratio of the
intensities gives a comparison factor. A reference point is m = 100,
corresponding to an intensity of 2.65 x 10^-6 lumens.
Absolute Magnitude, M
how we define absolute magnitude (M).
It depends on the star's luminosity, which is a measure of its brightness:
L = 4 pi R^2 s T^4
R is the radius of the body emitting light, s is the Stefan-Boltzmann
constant (5.67 x 10-8 W/m^2K^4) and T is the effective temperature (in
K) of the body.
constant (5.67 x 10-8 W/m^2K^4) and T is the effective temperature (in
K) of the body.
So, a star's luminosity depends on its size (radius, R) and absolute temperature (T).
If the star is 10 pm away, its M = m (by definition).
m – M = 5 log (d/10)
We let d = the distance (in pc), log is base 10, m is apparent
magnitude and M is absolute magnitude.
A problem: If d = 20 pc and m = +4, what is M? (2.5)
And another (more challenging):
If M = 5 and m = 10, how far away is the star? (100 pc)
Applets
http://lectureonline.cl.msu.edu/~mmp/kap25/Snell/app.htm
http://www.physics.uoguelph.ca/applets/Intro_physics/refraction/LightRefract.html
http://www.physics.metu.edu.tr/~bucurgat/ntnujava/Lens/lens_e.html
For lenses and mirrors, in general - probably more complicated than you need, but this is what is going on in lenses (and mirrors).
http://www.physics.uoguelph.ca/applets/Intro_physics/refraction/LightRefract.html
http://www.physics.metu.edu.tr/~bucurgat/ntnujava/Lens/lens_e.html
For lenses and mirrors, in general - probably more complicated than you need, but this is what is going on in lenses (and mirrors).
Reflection and Refraction
Reflection - light "bouncing" off a reflective surface. This obeys a simple law, the law of reflection!
The incident (incoming) angle equals the reflected angle. Angles are generally measured with respect to a "normal" line (line perpendicular to the surface).
Note that this works for curved mirrors as well, though we must think of a the surface as a series of flat surfaces - in this way, we can see that the light can reflect in a different direction, depending on where it hits the surface of the curved mirror. More to come here.
Refraction revisited:
Refraction is much different. In refraction, light enters a NEW medium. In the new medium, the speed changes. We define the extent to which this new medium changes the speed by a simple ratio, the index of refraction:
n = c/v
In this equation, n is the index of refraction (a number always 1 or greater), c is the speed of light (in a vacuum) and v is the speed of light in the new medium.
The index of refraction for some familiar substances:
vacuum, defined as 1
air, approximately 1
water, 1.33
glass, 1.5
polycarbonate ("high index" lenses), 1.67
diamond, 2.2
The index of refraction is a way of expressing how optically dense a medium is. The actual index of refraction (other than in a vacuum) depends on the incoming wavelength. Different wavelengths have slightly different speeds in (non-vacuum) mediums. For example, red slows down by a certain amount, but violet slows down by a slightly lower amount - meaning that red light goes through a material (glass, for example) a bit faster than violet light. Red light exits first.
In addition, different wavelengths of light are "bent" by slightly different amounts. This is trickier to see. We will explore it soon.
Electromagnetic radiation
Light and other types of electromagnetic radiation
You're most familiar with visible light - ROYGBV. This is a tiny sliver of the huge variety of electromagnetic waves given off by things that emit light naturally (stars) and those that generally absorb and reflect or re-emit light (planets, us, etc.)
All forms of these "waves" are called electromagnetic waves, since the wave consists of an electric component and a magnetic component. These waves can be represented on a chart of electromagnetic radiation (waves being emitted) that goes from low frequency waves (with long wavelengths) to high frequency waves (with short wavelength).
All of these waves travel at that same speed in a vacuum (or near vacuum like space) - the speed of light (c).
The product of frequency and wavelength is always the same value - the speed of light.
Speed of light = frequency (f) x wavelength (l)
c = f l
You're most familiar with visible light - ROYGBV. This is a tiny sliver of the huge variety of electromagnetic waves given off by things that emit light naturally (stars) and those that generally absorb and reflect or re-emit light (planets, us, etc.)
All forms of these "waves" are called electromagnetic waves, since the wave consists of an electric component and a magnetic component. These waves can be represented on a chart of electromagnetic radiation (waves being emitted) that goes from low frequency waves (with long wavelengths) to high frequency waves (with short wavelength).
All of these waves travel at that same speed in a vacuum (or near vacuum like space) - the speed of light (c).
The product of frequency and wavelength is always the same value - the speed of light.
Speed of light = frequency (f) x wavelength (l)
c = f l
Thursday, June 13, 2013
Assignment #2
Assume that g = 10 m/s/s for these problems. You may need a calculator, though you shouldn't on the quiz.
1. Consider a ball dropped from rest. How fast would it be traveling after 2.5 seconds of freefall?
2. In the problem above, how far would the ball have fallen in this 2.5 seconds?
3. If you dropped the same ball from the same height on the Moon, would it take a longer or shorter time to hit the surface?
4. Why are there high altitude directions on boxes of food that has to be boiled? (Take a look at a box of macaroni and cheese, if possible.)
5. Thought question. Knowing what Galileo discovered through his telescope, what do you think was the convincing evidence (for him, or you, if you prefer) that Earth went around the Sun? In other words, Galileo's telescopic discoveries helped him embrace the Copernican worldview. Why?
6. Imagine two stars in space a certain distance apart. If there distance is tripled (made larger 3 times the original distance), what exactly would happen to the gravitational force between them?
7. Recall the two short video clips about the inclined planes with the bells. What was their significance?
8. Why exactly do two bodies with very different masses fall to the ground with the same acceleration? (Why would a bowling ball and tennis ball hit the ground at the same time?)
9. What is "freefall"? We didn't really discuss this in class, but give it some thought.
10. Why do astronauts in orbit around the Earth have to exercise so much?
A thought question that does not have an easy answer - really just for you to play with. It will not be represented on a quiz. Around the year 1600, virtually no one believed in a heliocentric universe. By the year 1700, virtually everyone did. What could have possibly caused such a dramatic change in public opinion?
1. Consider a ball dropped from rest. How fast would it be traveling after 2.5 seconds of freefall?
2. In the problem above, how far would the ball have fallen in this 2.5 seconds?
3. If you dropped the same ball from the same height on the Moon, would it take a longer or shorter time to hit the surface?
4. Why are there high altitude directions on boxes of food that has to be boiled? (Take a look at a box of macaroni and cheese, if possible.)
5. Thought question. Knowing what Galileo discovered through his telescope, what do you think was the convincing evidence (for him, or you, if you prefer) that Earth went around the Sun? In other words, Galileo's telescopic discoveries helped him embrace the Copernican worldview. Why?
6. Imagine two stars in space a certain distance apart. If there distance is tripled (made larger 3 times the original distance), what exactly would happen to the gravitational force between them?
7. Recall the two short video clips about the inclined planes with the bells. What was their significance?
8. Why exactly do two bodies with very different masses fall to the ground with the same acceleration? (Why would a bowling ball and tennis ball hit the ground at the same time?)
9. What is "freefall"? We didn't really discuss this in class, but give it some thought.
10. Why do astronauts in orbit around the Earth have to exercise so much?
A thought question that does not have an easy answer - really just for you to play with. It will not be represented on a quiz. Around the year 1600, virtually no one believed in a heliocentric universe. By the year 1700, virtually everyone did. What could have possibly caused such a dramatic change in public opinion?
Tonight's Notes
Galileo Galilei
1609, telescope
· Moon has craters
· Way more stars than thought
· Jupiter has 4 moons – Io, Europa, Ganymede, Callisto…. Jupiter actually has over 60 moons.
· Saturn has rings!
· Venus goes through phases (like the Moon)
· Sun has spots! (Sunspots)
· Siderius Nuncius (Starry Messenger)
See also Galileo’s book: Dialogue on Two World Systems (1632)
Newton, 1642-1727
· Laws of motion – inertia, F=ma, action/reaction
· Calculus
· Binomial theorem
· Alchemy (oops)
· Rules of optics
· White light is made of colors (prism)
· Reflecting telescope (used a mirror)
· Explained tides
· Universal gravity
· Rules of reasoning in philosophy
Principia Mathematica Naturalis Philosophae, 1687
Fg = G m1 m2 / d2
Newton’s law of universal gravitation
m1 = first mass
m2 = second mass
G = universal constant of gravitation (a very tiny number, 6.67 x 10-11)
d = distance between masses
This is an INVERSE SQUARE law – meaning that as the distance increases, the force gets smaller at a rate of 1 over the distance squared. For example, if you double the distance, the new force is ¼ the original. Triple the distance and the new force is 1/9 the original.
Local gravitation (g)
On Earth, near the surface:
g is approximately 9.8 m/s/s (or around 10 m/s/s). This means that a freely-falling object increases its speed by roughly 10 m/s with every second of freefall. Or conversely, if a body is projected upward, it loses roughly 10 m/s upward with each second of travel up.
This looks like this for a falling object:
After 1 second, its speed is 10 m/s.
After 2 seconds, its speed is 20 m/s.
After 3 seconds, 30 m/s
Or if you like equations:
v = g t
The distance that an object falls is a bit trickier to follow. I will skip the derivation, but it is given by this formula:
d = ½ g t2
Or, d = 5t2 , near the surface of the Earth.
So, after 1 second, an object falls 5 m.
After 2 seconds, d = 20 m.
After 3 seconds, d = 45 m.
After 4 seconds, d = 80 m.
Notice how the distance is climbing up exponentially. If you graphed distance versus time, you’d get a parabola.
Now for Galileo’s odd number’s rule (just for mathematical fun) – see the earlier blog entry.
With increased altitude, g becomes progressively (but slowly) weaker.
On the Moon, local gravity (at the Moon’s surface) is approximately 1/6 that of Earth.
On Venus, it’s around 9/10 that of Earth.
On Jupiter, it’s around 2.5 times that of Earth.
Local gravity (g) can be calculated with this expression:
g = G Mplanet / r2
Where G is the same constant as before, Mplanet is the mass of your planet and r is the radius of your planet.
So, do all bodies experience the same local gravity? Why?
FYI:
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