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Physics, Astronomy & Cosmology / Re: Are clocks ticking faster where gravity is stronger?
« on: 08/05/2018 07:23:46 »The slight increase in local g at the Andes is more than offset by the increase in R from the center the the Earth. The Andes are gravitationally "uphill" from Western Australia, regardless of the fact that g might be slightly higher in the Andes. Extreme case in point. If you were able to drill a hole to the center of the Earth, at the bottom g would be 0, yet the escape velocity from the bottom of the hole would be greater than that at the surface. A ballistic object would lose velocity climbing out of the hole, but would still need to be moving at surface escape velocity when it got the surface in order to escape Earth's gravity. And a clock at the center of the Earth would run slower than one at the surface, despite being at zero g.
It is actually 'the offset' that I'm particularly interested in. Could you by any chance give me some maths for the equatorial bulge showing this offset?
OK as a matter of curiosity - so you say that escape velocity would have to be greater from centre of earth is g=0, than it would be at surface of earth.
But if we look at how much thrust would be needed to achieve that velocity from a 0g start point, surely the 'work done' will be the same?
If same amount of thrust is applied at 0g centre of earth as is applied at surface of earth to achieve escape velocity, then isn't the rocket traveling at a speed that escape velocity is still possible from by the time it reaches the surface? ie: same amount of work.
Ignoring the fact that the difference in air density between the Andie's and Western Australia will cause a rocket engine to perform differently, and ignoring that a rocket doesn't maintain a trajectory of flight that is directly above its launch site - a rocket taking off with same thrust at the Andie's, compared to the rocket taking off with same thrust at Western Australia, will not reach the 'same speed' due to the Andie's having more downwards pull than Western Australia.
In order for the rockets to achieve the same amount of 'distance' (not height), in the same amount of time (as per a distant observer), won't the Andie's rocket have to 'work' harder?