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Is the force of gravity experienced by an object, higher, if its moving (Eg: in a perpendicular/tangential direction to the center of gravity), as compared to when it is at rest?

My understanding is that it it remains the same but wanted to check anyhow.

For example, if it was indeed the case, then satellites in orbits (or comets/asteroids passing by) would experience a greater force of gravity as compared to what they would have experience if they had simply been suspended in space at the same point (although it may not be easy to measure this effect since velocity tends to act against the effects of gravitational pull).

One way to test this would be to have a spinning flywheel be weighted against one that is not and observe if both are equal (we could have two flywheels, one spinning clockwise and the other anti-clockwise to cancel the angular momentum).

Also given the low value for gravitational constant, the two flywheels would have to be quite massive (probably the scale of a moon or equivalent) for it to be even measurable. As such believe its unlikely that an experiment similar to the 'Michelson–Morley experiment' on aether has been conducted and while it may have been possible to observe in astronomy, its unlikely that two objects with sufficient difference in angular momentum have been observed under the influence of gravity for us to have learnt from it (calculating angular momentum of remote objects would itself be a challenge).

Note :
Have seen a few examples related to general/special relativity (here) but believe this question belongs to the classical physics domain (please do correct me if my understanding is wrong).

Regards,
Ravindra

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Is the force of gravity experienced by an object, higher, if its moving (Eg: in a perpendicular/tangential direction to the center of gravity), as compared to when it is at rest?

It's not.

In classical physics (unlike in somewhat stronger gravitational fields) and for point-like objects (and sources), gravitational force felt by a moving object with mass $m_2$ is simply

$$\mathbf{F}_{21} = -G\frac{m_1m_2}{|\mathbf{r}_{12}|^2}{\mathbf{\hat r}}_{12}$$

where $m_1$ is the mass of the source of gravity, $\mathbf{r}_{12}$ is the position vector from the source to the object and ${\mathbf{\hat r}}_{12}$ is the unit vector from the source in the direction of the object, according to Newton's gravitational law.

It's an empirical observation - in times of Newton, there was no reason to suspect and no way to measure velocity playing any role.

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