In the orbital velocity formula v = sqrt(GM/r), what does GM stand for?

• A. The gravitational field strength
• B. The product GM, where G is the gravitational constant and M is the central mass
• C. The gravitational potential energy
• D. The angular momentum

Answer: (B)

GM is the gravitational parameter of the central body: the product of the gravitational constant G and the mass M being orbited. In the orbital velocity formula, v = sqrt(GM/r), this single quantity encapsulates how strong gravity is for that body. You can see where it comes from by equating centripetal acceleration to gravitational acceleration: v^2/r = GM/r^2, which gives v = sqrt(GM/r).

Check the units to see why this makes sense: G has units of m^3/(kg·s^2) and M is in kg, so GM has units of m^3/s^2. Dividing by r (meters) gives m^2/s^2, and taking the square root yields m/s, perfect for velocity. GM is often written as μ or GM for the central object, such as GM_sun.

It’s not the gravitational field strength, which is GM/r^2, and it’s not gravitational potential energy, which is -GMm/r, and not angular momentum, which is L = mvr.