Which formula represents the orbital (circular) velocity of a satellite around a central mass M?

• A. L = mvr
• B. v = sqrt(GM/r)
• C. F = ma
• D. v = 2π r / T

Answer: (B)

In a circular orbit, gravity provides the centripetal force that keeps the satellite moving in a circle. The gravitational pull toward the center is GMm/r^2, and the required centripetal force is m v^2 / r. Setting them equal gives GMm/r^2 = m v^2 / r, which simplifies to v^2 = GM/r, so v = sqrt(GM/r). This shows why the velocity depends on the central mass and the radius of the orbit: closer in (smaller r) means faster orbital speed, while larger r means slower speed. The other relations relate to different ideas: angular momentum L = m v r is a separate quantity, F = ma is the general form of Newton's second law, and v = 2π r / T expresses velocity in terms of orbital circumference and period, which is useful in a different context but not the direct expression for orbital speed in terms of GM and r.