what would be the mass required to keep an object with a mass of 250kg orbiting at a constant distance of 100km with a linear velocity of 100m/s?

the linear speed of an orbiting body is given by the equation sqrt(GM/2r) where M is the mass of the attracting body, G is the gravitational constant and r is the distance between the two bodies' centres of mass. The mass of the orbiting body is irrelevant yet is sometimes put into questions as red herrings to truly test the knowledge of students. To solve this all we need to do is rearrange the equation to give us M = 2v²r/G

We know all of the numbers on one side of the equation so all we have to do is plug in the numbers, v = 100m/s r = 100,000m                                G = 6.67x10^-11 Nm²kg^-2 . so after plugging all of the numbers into the equation we get that the mass required to keep an object orbiting at 100km at 100m/s is 3.0x10¹⁹kg or roughly 0.0005 x the mass of the earth