Explain how orbital altitude relates to orbital velocity in circular orbits.

Explain how orbital altitude relates to orbital velocity in circular orbits.

• A. Higher altitude requires higher orbital velocity.
• B. Higher altitude circular orbits require lower orbital velocity; velocity decreases as the radius increases.
• C. Velocity is independent of altitude in circular orbits.
• D. Only eccentric orbits show a velocity change with altitude.

Answer: (B)

In a circular orbit, gravity provides the exact centripetal force needed to keep an object moving in a circle. The balance equation is GMm/r^2 = m v^2 / r, which simplifies to v^2 = GM / r. So the orbital speed v is proportional to 1 over the square root of the radius. As altitude increases, the orbital radius r increases, and the required speed decreases. Therefore higher altitude circular orbits require lower orbital velocity, with velocity decreasing as radius increases. It's not independent of altitude, and circular orbits do have velocity that depends on radius. The idea that only eccentric orbits show velocity changes is incorrect for circular orbits, where the speed is set by the radius to maintain circular motion.

In a circular orbit, gravity provides the exact centripetal force needed to keep an object moving in a circle. The balance equation is GMm/r^2 = m v^2 / r, which simplifies to v^2 = GM / r. So the orbital speed v is proportional to 1 over the square root of the radius. As altitude increases, the orbital radius r increases, and the required speed decreases. Therefore higher altitude circular orbits require lower orbital velocity, with velocity decreasing as radius increases.

It's not independent of altitude, and circular orbits do have velocity that depends on radius. The idea that only eccentric orbits show velocity changes is incorrect for circular orbits, where the speed is set by the radius to maintain circular motion.