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Greetings all,
Taken in the limit of a small distance where the Earth appears flat, does a stationary object (relative to the Earth) disagree with an object moving horizontally about the force due to gravity, g? (Again, take the limit of having no altitude, so g is constant.) For example, the stationary object feels g as 9.8 m/s^2. Say a bullet is traveling at .99c. I assume it feels g as 9.8 m/s^2. However, I believe the stationary object would report there's another force acting on the bullet from it's perspective (or g is not equal to 9.8). The reason is that the two would disagree on the distance between any two points A and B that the bullet moves between. The bullet doesn't feel that it falls very far because it traveled a much shorter distance. The outside observer agrees that it doesn't fall very far and therefore says there's another force acting on the bullet. I'm aware of the effects of general relativity and time dilation due to gravitational fields, but I think we can neglect this because they are at the same height (at least for some tiny amount of time). Am I right that both the bullet and the stationary object feel g as 9.8, but the outside observer disagrees that the bullet is feeling g as 9.8? (Alternatively, the bullet could say it doesn't feel g as 9.8, but the stationary object sees g as 9.8 for the bullet, I suppose.) What is this called? Is this something used to derive general relativity? (It seems too simple to really be GR to me -- no tensor horrors :-) ).
Taken in the limit of a small distance where the Earth appears flat, does a stationary object (relative to the Earth) disagree with an object moving horizontally about the force due to gravity, g? (Again, take the limit of having no altitude, so g is constant.) For example, the stationary object feels g as 9.8 m/s^2. Say a bullet is traveling at .99c. I assume it feels g as 9.8 m/s^2. However, I believe the stationary object would report there's another force acting on the bullet from it's perspective (or g is not equal to 9.8). The reason is that the two would disagree on the distance between any two points A and B that the bullet moves between. The bullet doesn't feel that it falls very far because it traveled a much shorter distance. The outside observer agrees that it doesn't fall very far and therefore says there's another force acting on the bullet. I'm aware of the effects of general relativity and time dilation due to gravitational fields, but I think we can neglect this because they are at the same height (at least for some tiny amount of time). Am I right that both the bullet and the stationary object feel g as 9.8, but the outside observer disagrees that the bullet is feeling g as 9.8? (Alternatively, the bullet could say it doesn't feel g as 9.8, but the stationary object sees g as 9.8 for the bullet, I suppose.) What is this called? Is this something used to derive general relativity? (It seems too simple to really be GR to me -- no tensor horrors :-) ).