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Could a bullet be made something that could go from orbit to Earth's surface?
I wrote
The math is as follows: If you are in a cirular orbit at altitude h, you are r = h + R from the center of earth (with R = 6378 km) and you are moving with respect to the center of earth at a speed of v = sqrt(k/r), where k = 398601 km^3/s^2 is the gravitational constant for earth (also called GM). Now you want to change your orbit into an elliptical one with the highest point at radius r, and the lowest at s = 100km + R. In such an orbit you would at the highest point need an orbital speed of w = sqrt(k*(2/r-1/s)) which means that you must change your speed with dv = v - w in order to change from the circular orbit to the elliptical orbit. If you use the numbers as I have written them above, then the speed unit will be km/s. Somehow I managed to confuse "s" with "a" (which equals (r+s)/2) on the back of my envelope, so the correct form is w = sqrt(k*(2/r-2/(r+s))). Sorry about that. -- Filip Larsen |
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