An artificial satellite revolves around a planet for which gravitational force (F) varies with distance r from its centre as - Physics - Gravitation

Question

An artificial satellite revolves around a planet for which
gravitational force (F) varies with distance r from its centre as F
is directly proportional to r^2 then how is orbital speed related
to r?

Ravi Gupta · Accepted Answer

F is directly proportional to the square of the radiusF ∝r2F = kr2where k is the proportionality constant
when planet revolves, centrepetal force will act on the planetF = mv2rmv2r=kr2v2 = kr3mv= kmr3/2v∝r3/2

An artificial satellite revolves around a planet for which gravitational force (F) varies with distance r from its centre as F is directly proportional to r^2 then how is orbital speed related to r?