Put your observatory here: Although a single planet of given mass m in orbit abo
ID: 1311896 • Letter: P
Question
Put your observatory here: Although a single planet of given mass m in orbit about let's say, a star of mass M, with a known orbital radius can have only one period of its orbit for that given radius, if a third object were placed at certain special points within this system (i.e. the Lagrange points), then this third object object (with two forces of gravity acting on it from the star and then the planet) can have the same period of orbit as the planet has about the star. Find the radius of this third object from the star such that this could occur. One position would be in between the star and the planet and another position would be outside of the planet and star; both of those positions would be along a line joining the star and planet at any given instant. Find these two points. There are other Lagrange points but that's not this problem.
Explanation / Answer
G is, as far as we know, constant through space and time, although there is speculation that it may have had other values at other times, or may in future do so. The fact that your equation can be re-arranged to have the constant, G, on one side, and lots of variables on the other side is no big deal. If you think about, pretty much any equation containing a constant can be rearranged in the same way. For example, Circumference = 2 x pi x radius can be rearranged as 2 = Circumference/(radius x pi). The fact that the equation can be rearranged in this way doesn't make 2 variable, any more than (as far as we know) G is variable. It's just the way algebra works,
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