Question

The orbital period of GPS satellites is determined by the ................. of their orbits.

• A. semi-major axis
• B. eccentricity
• C. inclination
• D. semi-major axis, inclination and eccentricity

Hint:

Same $a$ $⇒$ same period: two orbits around Earth with identical semi-major axis (even with different $e$ or $i$) have identical $T$.

Answer 1

The Correct Option is A

From Kepler’s third law for two-body motion, \[ T=2\pi\sqrt{\frac{a^{3}}{\mu}}, \] where $T$ is the orbital period, $a$ the semi-major axis, and $\mu$ Earth’s gravitational parameter. $T$ depends only on $a$ (for a given central body), not on eccentricity or inclination. Hence (A).