# Tag Info

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I was trying to solve a similar problem, and did, with help on StackOverflow. My question was here: http://stackoverflow.com/questions/16501182/find-first-root-of-a-black-box-function-or-any-negative-value-of-same-function I asked it more abstractly. The way I saw it, you have a ship and moon (for example), and for different values of time they have a ...

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This is not my field, but the question is interesting so I'll give you my best answer. The sphere of influence of an isolated astronomical body (in this case the binary stars, treated as a unit) is not well-defined; therefore, some of the forthcoming argument requires more information about the context in which you are studying the binary system (like the ...

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Regarding the Corona program, wikipedia says The first satellites in the program orbited at altitudes 100 miles (160 km) above the surface of the Earth, although later missions orbited even lower at 75 miles (121 km)). and continues to say Corona orbited in very low orbits to enhance resolution of its camera system. But at perigee (the lowest ...

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About 200 kilometers is a good benchmark. Even complete satellites (as opposed to small, high-drag fragments) will de-orbit within days (i.e. ~100 orbits) from that height. Since drag depends for a large part on pressure and pressure sharply drops at these heights, the most important height is the periapsis (lowest point in orbit). However, a satellite with ...

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It's often worth considering an extreme example. Suppose, for instance, that we put virtually all of the mass of the moon into four extremely dense "mascons" located near the surface and at the vertices of a square (whose center would, therefore, necessarily coincide with the center of the moon.) Now consider the net gravitational force on a satellite as ...

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The replacement of a body, for gravitational purposes, by the same mass located at the center of mass, is based on the assumption that the body is spherically symmetric. This is usually a good approximation for large body, but not a perfect one. The earth can be considered as spherical, then as a sphere with an added equatorial bulge, and then as a ...

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If the two objects are equal in mass (or close to it), both orbit their barycenter, which would be a point outside either body. If one object suddenly loses half its mass, the COM of the binary system moves with respect to the current locations of both objects, resulting in changes to acceleration for both ($a=\frac{GM}{ r^2}$, where r is distance to ). i.e, ...

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If you remove a bit of moon and leave the rest with the same velocity, it will continue to follow the same orbit. Since you are carrying away some of the mass, as you carry it away it will exert a gravitational force on the moon, which could change the velocity. You are correct that cutting the mass in half will cut the gravitational force in half, but so ...

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