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Gravity Variant on a Tether
My questions concerns the gravity gradient on an orbiting tether, let's say
1,000 km long. The center of mass for the tether would determine its orbital velocity so the portion of the tether above the c.o.m. would be travelling faster than its orbital velocity would require and the tether below c.o.m. would be travelling slower than its orbital velocity would require. In a microgravity environment, the sensation of freefall is experienced because the forward orbiting velocity is equal to the downward pull of gravity. What happens when you are below the tether and your orbital velocity is slower than it should be and is thus less than the pull of gravity? Will freefall not exist in the stations or gondolas below the tether's center of mass? Also, above the tether's c.o.m. would gravity be pulling you "upwards" away from the Earth? I hope I've gotten the fundamentals correct. TangoMan |
#2
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Gravity Variant on a Tether
TangoMan wrote in message news:SfcBb.617057$9l5.135061@pd7tw2no...
My questions concerns the gravity gradient on an orbiting tether, let's say 1,000 km long. The center of mass for the tether would determine its orbital velocity so the portion of the tether above the c.o.m. would be travelling faster than its orbital velocity would require and the tether below c.o.m. would be travelling slower than its orbital velocity would require. In a microgravity environment, the sensation of freefall is experienced because the forward orbiting velocity is equal to the downward pull of gravity. What happens when you are below the tether and your orbital velocity is slower than it should be and is thus less than the pull of gravity? You'll fall. Assume the non-rotating tether is in a circular orbit and you're hanging from the lower end of the tether. If you let go, you will find yourself at the high point (apogee) of an elliptical orbit and falling toward the low point (perigee) of that orbit, which we can hope is not within the atmosphere. One orbit revolution later you will find yourself rising back toward apogee and,hopefully, within grabbing distance of the tether's end, which has also completed one revolution around the Earth. Will freefall not exist in the stations or gondolas below the tether's center of mass? No. Also, above the tether's c.o.m. would gravity be pulling you "upwards" away from the Earth? Yes. I hope I've gotten the fundamentals correct. Yes. |
#3
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Gravity Variant on a Tether
TangoMan wrote in message news:SfcBb.617057$9l5.135061@pd7tw2no...
My questions concerns the gravity gradient on an orbiting tether, let's say 1,000 km long. The center of mass for the tether would determine its orbital velocity so the portion of the tether above the c.o.m. would be travelling faster than its orbital velocity would require and the tether below c.o.m. would be travelling slower than its orbital velocity would require. In a microgravity environment, the sensation of freefall is experienced because the forward orbiting velocity is equal to the downward pull of gravity. What happens when you are below the tether and your orbital velocity is slower than it should be and is thus less than the pull of gravity? You'll fall. Assume the non-rotating tether is in a circular orbit and you're hanging from the lower end of the tether. If you let go, you will find yourself at the high point (apogee) of an elliptical orbit and falling toward the low point (perigee) of that orbit, which we can hope is not within the atmosphere. One orbit revolution later you will find yourself rising back toward apogee and,hopefully, within grabbing distance of the tether's end, which has also completed one revolution around the Earth. Will freefall not exist in the stations or gondolas below the tether's center of mass? No. Also, above the tether's c.o.m. would gravity be pulling you "upwards" away from the Earth? Yes. I hope I've gotten the fundamentals correct. Yes. |
#4
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Gravity Variant on a Tether
TangoMan wrote in message news:SfcBb.617057$9l5.135061@pd7tw2no...
What happens when you are below the tether and your orbital velocity is slower than it should be and is thus less than the pull of gravity? Will freefall not exist in the stations or gondolas below the tether's center of mass? Also, above the tether's c.o.m. would gravity be pulling you "upwards" away from the Earth? I hope I've gotten the fundamentals correct. The net force on you is as you say. If you are attached to a tether you feel like "up" is toward the center of mass of the tether. So if you are above the tethers c.o.m then your "down" is a normal guys "up". You should not say "gravity" is pulling you away from the Earth. It is that the centrifugal force from your orbital speed (v^2/r) is more (or less if below) than the gravitational force on you and the tether is making up the difference. Since you can not push on a rope, if you at the end of a tether it is going to be pulling on you and you will feel like down is away from the tether. -- Vince |
#5
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Gravity Variant on a Tether
TangoMan wrote in message news:SfcBb.617057$9l5.135061@pd7tw2no...
What happens when you are below the tether and your orbital velocity is slower than it should be and is thus less than the pull of gravity? Will freefall not exist in the stations or gondolas below the tether's center of mass? Also, above the tether's c.o.m. would gravity be pulling you "upwards" away from the Earth? I hope I've gotten the fundamentals correct. The net force on you is as you say. If you are attached to a tether you feel like "up" is toward the center of mass of the tether. So if you are above the tethers c.o.m then your "down" is a normal guys "up". You should not say "gravity" is pulling you away from the Earth. It is that the centrifugal force from your orbital speed (v^2/r) is more (or less if below) than the gravitational force on you and the tether is making up the difference. Since you can not push on a rope, if you at the end of a tether it is going to be pulling on you and you will feel like down is away from the tether. -- Vince |
#6
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Gravity Variant on a Tether
In article SfcBb.617057$9l5.135061@pd7tw2no,
TangoMan wrote: What happens when you are below the tether and your orbital velocity is slower than it should be and is thus less than the pull of gravity? Will freefall not exist in the stations or gondolas below the tether's center of mass? Correct, it does not. You're experiencing what are otherwise known as tidal effects. For very sensitive experiments, this can be an issue even in sizable structures like ISS -- the locations of the ISS lab modules within the station were chosen with this in mind. Also, above the tether's c.o.m. would gravity be pulling you "upwards" away from the Earth? Correct again, although it's more properly a gravity *gradient* that's pulling you upward. -- MOST launched 30 June; first light, 29 July; 5arcsec | Henry Spencer pointing, 10 Sept; first science, early Oct; all well. | |
#7
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Gravity Variant on a Tether
In article SfcBb.617057$9l5.135061@pd7tw2no,
TangoMan wrote: What happens when you are below the tether and your orbital velocity is slower than it should be and is thus less than the pull of gravity? Will freefall not exist in the stations or gondolas below the tether's center of mass? Correct, it does not. You're experiencing what are otherwise known as tidal effects. For very sensitive experiments, this can be an issue even in sizable structures like ISS -- the locations of the ISS lab modules within the station were chosen with this in mind. Also, above the tether's c.o.m. would gravity be pulling you "upwards" away from the Earth? Correct again, although it's more properly a gravity *gradient* that's pulling you upward. -- MOST launched 30 June; first light, 29 July; 5arcsec | Henry Spencer pointing, 10 Sept; first science, early Oct; all well. | |
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