Can Satellites Measure Earth's Geode Using Velocity Instead of Position?

[dodo]

Hello, layman question here.

Suppose a spaceship approaches a highly massive body, at great speed; it violently swings around the body and comes back in less than a minute. All in a free trajectory, with thrusters never applied.

The question is: would the occupants of the ship be crushed against the outward wall of the capsule? Or the centrifugal force would be perfectly balanced with the body's attraction, and thus the occupants be all the time in free-falling ingravity?

The issue came in the context of satellites measuring the Earth's geode, by detecting tiny variations in their own orbits. A colleague of mine argued that, since the satellite follows a geodesic, accelerometers on board would not pick anything; thus two satellites are needed, one closely following the other, and from measures of their relative distance, variations on their orbit can be indirectly deduced.

 

[Dale]

The question is: would the occupants of the ship be crushed against the outward wall of the capsule? Or the centrifugal force would be perfectly balanced with the body's attraction, and thus the occupants be all the time in free-falling ingravity?

Assuming that the ship is small enough that tidal forces can be neglected then the occupants would be free-falling and would not detect anything and they would certainly not describe it as a "violent swing".

 

[JustinLevy]

The question is: would the occupants of the ship be crushed against the outward wall of the capsule? Or the centrifugal force would be perfectly balanced with the body's attraction, and thus the occupants be all the time in free-falling ingravity?

They are free-falling the whole time (as defined specifically in the problem, since you said no other forces are involved).

Since the spaceship isn't a point, there could be tidal forces on it (in Newtonian terms, the force of gravity isn't the same on all parts of the ship because it is of finite size). In realistic situations this would very very likely be too small to measure.

The issue came in the context of satellites measuring the Earth's geode, by detecting tiny variations in their own orbits. A colleague of mine argued that, since the satellite follows a geodesic, accelerometers on board would not pick anything; thus two satellites are needed, one closely following the other, and from measures of their relative distance, variations on their orbit can be indirectly deduced.

I would agree with your colleague. Having two satellites is in essence a way to make the size of the satellite larger, to make the effects of the tidal forces more noticeable.

 

[D H]

The issue came in the context of satellites measuring the Earth's geode, by detecting tiny variations in their own orbits. A colleague of mine argued that, since the satellite follows a geodesic, accelerometers on board would not pick anything; thus two satellites are needed, one closely following the other, and from measures of their relative distance, variations on their orbit can be indirectly deduced.

That is essentially what the GRACE project does. That said, scientists had developed very good estimates of the Earth's gravitational field prior to GRACE. One satellite suffices coupled with measurements of the satellite's state as a function of time. The best models of the Moon's gravitational field, LP150Q, for example, was formed from measurements of just one satellite orbiting the Moon: the Lunar Prospector.

 

[JustinLevy]

One satellite suffices coupled with measurements of the satellite's state as a function of time.

To be explicit, the 'state' here is the relative position of the satellite. It is just relative to the body being orbitted, instead of relative to another satellite as the colleague suggested.

 

[D H]

No necessarily position. Velocity works quite nicely. NASA's Deep Space Network does a much better job measuring velocity than position in general, and does an extremely good job of measuring range rate in particular. The lunar gravity model was formed based primarily on doppler shifts in the signal transmitted by the Lunar Prospector satellite. For more, read http://lunar.arc.nasa.gov/printerready/science/newresults/dopp-ge.html.