Why Do Objects Float in Space Station (SS)?

paulfr
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I am confused about why astronauts and objects around them float in The Space Station [SS].

In space a long way from massive bodies, objects float.
In free fall, objects behave as if in a Gravity free region; they also float.

But the SS has 90% of the Gravity that exists on Earth.
PLUS
The SS is not accelerating in orbit, so its velocity is constant.

So shouldn't objects sink toward the Earth
AND
move toward the rear of the SS, opposite the direction of motion
[just as a rock in a wagon appears to move to the back of the wagon].

Which assumption or reasoning is flawed here ?
 
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This doesn't have anything to due with GR at the moment, it's purely classical physics. Your arguments are purely Newtonian.

If the space station was not accelerating, it would be moving in a straight line. But it's not moving in a straight line, it's moving in a circular orbit.

Thus, the space station is accelerating, because it's not moving in a straight line. The type of acceleration associated with moving in a circle is known as "centriptal acceleration". The centriptal acceleration of the space station is equal to the Earth's gravity at its height.
 
Yes the Centripetal Acceleration is created by Gravity.
So the SS is in free fall vertically.
That would explain the floating objects vertically.

But the SS must also fire engines perpendicular to the fall to stay
in orbit. If it does this on a continuous basis, then objects would
appear to move to the back of the SS opposite the direction of
horizontal acceleration.
If they fire only intermittently to maintain orbit height then
the motion when not accelerating is inertial and again objects float.

BTW, this Q came about because Einstein's thought process
about GR began with his Equivalence Principle of Gravity and Acceleration.
Free fall is part of the reasoning that led him to GR and geodesics.
 
paulfr said:
But the SS must also fire engines perpendicular to the fall to stay
in orbit.
While they fire the engines, the station is not in free fall anymore, so the free falling astronauts accelerate relative to the station.

paulfr said:
BTW, this Q came about because Einstein's thought process
about GR began with his Equivalence Principle of Gravity and Acceleration.
Free fall is part of the reasoning that led him to GR and geodesics.
I don't see what our question has to do with Newtonian gravity vs. GR. Both models explain the relative acceleration between station and astronauts.
 
paulfr said:
Yes the Centripetal Acceleration is created by Gravity.
So the SS is in free fall vertically.
That would explain the floating objects vertically.

But the SS must also fire engines perpendicular to the fall to stay
in orbit. If it does this on a continuous basis, then objects would
appear to move to the back of the SS opposite the direction of
horizontal acceleration.
If they fire only intermittently to maintain orbit height then
the motion when not accelerating is inertial and again objects float.

BTW, this Q came about because Einstein's thought process
about GR began with his Equivalence Principle of Gravity and Acceleration.
Free fall is part of the reasoning that led him to GR and geodesics.

The ISS is in free fall. It doesn't "fire engines perpendicular to the fall to stay
in orbit". It only does that occasionally to prevent orbit decay due to air drag and solar wind.
 
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From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...

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