Tim (17 Aug 2017 08:07 UTC) wrote:

>     > > An object motionless in a g field has constant potential energy,
>     > > hence no energy input is required to keep it there.
>     >
>     > I'm not 100% certain that this is the case.
>
>     It is the case.

I suspect that there is some usage of technical (as opposed to casual) language going
on here which is confusing the heck out of me, and perhaps others.

Please allow me to enquire further, and posit some test cases. Answers which use only
Newtonian physics preferred, if possible, but you may use calculus, at least for me :-)

1) Consider a helicopter hovering above a fixed point 1000 feet above the ground.
This is not in motion relative to the ground underneath it, nor to the local centre of
gravity (considered as a point source, and the rotation is not, I think, relevant), and yet
it is experiencing a force due to gravity. If it were to turn its engine off, it would
swiftly start converting some of its potential energy into kinetic, with sub-optimal results
(at least for the crew).

2) Consider a satellite in geosynchronous orbit. This is experiencing the force of gravity,
which is pulling it straight down (towards the local centre of mass) but it is also moving at
significant speed, in a straight line, and this is trying to make it move at right angles to
the force of gravity (this is often called centrifugal force).

These two forces balance out such that after some time the satellite has moved *outwards* from
a perfect circular orbit the exact same amount that the force of gravity has pulled it *inwards*
from that orbit. Hence the satellite stays in the same orbit. The satellite is at rest relative
to the ground underneath it, and hence to the local gravity gradient, but it is not at rest
relative to (say) the Earth-Moon-Sun frame of reference - it's whizzing around the Earth.

Were the satellite to decrease its forward momentum (eg by applying thrust against its direction
of motion), then a) it would see the Earth start to rotate underneath it; and b) it would, I think,
also start to convert some of its potential energy into kinetic, and people on the ground should
probably start to get worried :-)

3) Consider a satellite at the Earth-Moon L-1 point. This experiences two forces due to gravity:
one from the Earth and one from the Moon. These forces are equal, so the satellite goes nowhere
under the net force of gravity.

It watches the Earth rotate beneath it (but not the Moon, because the Moon is tidally locked).
Is such a satellite "motionless in a gravity field"? It's certainly motionless, and it's in a
gravity field, but it had two forces acting on it.

Please point out at this stage how and where my understanding is flawed.

All this is getting at the question of "if a helicopter needs to exert a downwards force in order
to counteract gravity, then wouldn't a hypothetical spaceship using a CG drive need to exert a
similar force?"

If someone(s) would be so kind as to explain, I would be most grateful. Thanks in advance.

Jonathan