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Gravity Variant on a Tether



 
 
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  #1  
Old December 9th 03, 05:32 AM
TangoMan
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Default 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  
Old December 9th 03, 03:00 PM
Bill Bogen
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Default 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  
Old December 9th 03, 03:00 PM
Bill Bogen
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Posts: n/a
Default 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  
Old December 9th 03, 05:29 PM
Vincent Cate
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Default 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  
Old December 9th 03, 05:29 PM
Vincent Cate
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Posts: n/a
Default 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  
Old December 9th 03, 08:16 PM
Henry Spencer
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Posts: n/a
Default 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  
Old December 9th 03, 08:16 PM
Henry Spencer
external usenet poster
 
Posts: n/a
Default 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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