# A Geodesic Motion

#### Sciolo

Summary
Would a body in free fall 'feel' a force acting upon it if the curvature of spacetime was suddenly increased?
My current understanding is that a person falling toward the surface of a planet with no atmosphere, would feel no force acting upon themselves even though they are accelerating relative to the planet. If the mass of the planet suddenly tripled while the person is in free fall, would the person 'feel' anything as a result or would they still feel no apparent force even though their rate of acceleration increases?

Thanks,
James

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#### Orodruin

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A point person in free fall will not feel any force. An extended person will be subject to tidal forces due to geodesic deviation.

If the mass of the planet suddenly tripled
It cannot do that. That would violate local energy-momentum conservation.

#### Ibix

How would the mass of the planet triple suddenly? Bear in mind that the Einstein field equations require that you respect local conservation of energy, so "the mass just appears out of nowhere" doesn't give a consistent scenario.

Assuming something like "a planet slams into it from the other side at near enough the speed of light that its gravitational influence wasn't felt earlier" then you'd get a gravitational wave passing through you and then you'd be in the region of higher curvature (and then dead from the debris of such a cataclysm shortly thereafter). You might (in principle, at least) feel the gravitational wave as it passes through you because this is tidal gravity. The geodesic motion of the different parts of your body would be in different directions, which I imagine might well feel like being pulled apart. However, the only actual forces in play are the internal structural forces of your body trying to keep itself together.

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#### A.T.

Would a body in free fall 'feel' a force acting upon it if the curvature of spacetime was suddenly increased?
The curvature is increasing all the time as you fall towards as massive body. It increases the tidal forces, leading to deformations which you could feel in extreme cases.

...would the person 'feel' anything as a result or would they still feel no apparent force...
To term "apparent force" usually refers to effects that you cannot "feel", and are due to the chosen coordinate system.

#### Sciolo

Thanks for the replies and explanations.

"Geodesic Motion"

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