In a circular orbit around a central body, which statement is true?

In a circular orbit around a central body, which statement is true?

• A. The distance to the central body remains constant and orbital speed is constant.
• B. The distance to the central body varies and orbital speed is constant.
• C. The distance to the central body remains constant while orbital speed varies.
• D. The distance to the central body varies and orbital speed varies.

Answer: (A)

In a circular orbit the distance to the central body stays fixed because the motion traces a constant-radius circle around the center. The gravitational pull provides exactly the centripetal acceleration needed to keep that motion going, so the speed doesn’t have to change as the object travels around. Mathematically, v^2 = GM/r, where GM is the central body's gravitational parameter and r is the fixed radius; with r and GM constant, the orbital speed is constant. The velocity’s direction, however, is continually changing as it moves along the circle, which creates the circular path. If the radius were allowed to vary, or the speed to change, the motion would no longer be a circular orbit.

In a circular orbit the distance to the central body stays fixed because the motion traces a constant-radius circle around the center. The gravitational pull provides exactly the centripetal acceleration needed to keep that motion going, so the speed doesn’t have to change as the object travels around. Mathematically, v^2 = GM/r, where GM is the central body's gravitational parameter and r is the fixed radius; with r and GM constant, the orbital speed is constant. The velocity’s direction, however, is continually changing as it moves along the circle, which creates the circular path. If the radius were allowed to vary, or the speed to change, the motion would no longer be a circular orbit.