Which method is used to determine orbital period from semi-major axis?

• A. Newton's law of universal gravitation
• B. Kepler's third law
• C. Hohmann transfer equations
• D. Vis-viva equation

Answer: (D)

The key idea is that the orbital period is set by the size of the orbit and the central gravitational parameter. Kepler's third law gives a direct link between how long a full orbit takes and the semi-major axis: P^2 = 4π^2 a^3 / μ, so P = 2π sqrt(a^3/μ). This is the simplest and most direct way to determine the period from the orbit’s size because it encapsulates how gravity and geometry set the timing of a revolution.

The vis-viva equation, v^2 = μ(2/r − 1/a), tells you the instantaneous speed at a given distance r along the orbit for that same path. It’s valuable for finding how fast you are moving at a point, but it doesn’t on its own give the orbital period without performing a full time integration around the orbit. The other concepts—while foundational or useful for planning transfers—do not provide a direct, straightforward link from semi-major axis to the orbital period as Kepler’s law does.