Final answer:
To rearrange v = 2πr/T to solve for the radius, multiply both sides by T to get vr = 2πr, then divide by 2π to isolate r, resulting in r = vT/(2π).
Step-by-step explanation:
To make the radius (r) the subject of the equation v = 2πr/T, where v is the orbital speed, T is the period (time for one orbit), and r is the average radius, we need to rearrange the formula. Start by multiplying both sides of the equation by T to get rid of the denominator, which gives us vr = 2πr. Next, divide both sides by 2π to solve for r, resulting in the equation r = vT/(2π). This allows you to find the average orbital radius when you know the orbital speed and period of an object.