The mass enclosed in any orbit can be estimated from the equation M(

Question

The mass enclosed in any orbit can be estimated from the equation M(<r) =v²r/ G. If the quantity (v²r) is constant, regardless of radius, where is the mass located?

Quizplus · Accepted Answer

If (v²r) is constant, it means that for any given radius, the product of v² and r is always the same. According to the equation M(<r) = (v²r) / G, the mass enclosed is directly proportional to the product of v² and r, and is independent of the shape of the mass distribution. Therefore, the only way for the mass enclosed to remain constant at all radii is if the mass is concentrated at the center (choice A).

The Mass Enclosed in Any Orbit Can Be Estimated from the Equation