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

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 relationship here is how the orbital period links to the size of the orbit. For a bound two-body system, the time it takes to go around once (the period) depends on the semi-major axis and the central body's gravitational parameter. The standard way to determine the period from the semi-major axis is Kepler's third law, written as P = 2π sqrt(a^3/μ), where μ = GM of the primary. This shows the period grows with the 3/2 power of the semi-major axis and directly uses a. The vis-viva equation, v^2 = μ(2/r − 1/a), describes the speed at a specific point along the orbit given a and μ. It is excellent for finding instantaneous velocity but does not directly provide the orbital period from the semi-major axis. Newton's law underpins these relations and can derive them, but the straightforward, commonly used method to get P from a is Kepler's law. Hohmann transfer formulas relate to changing orbits, not the basic P–a relationship.

The key relationship here is how the orbital period links to the size of the orbit. For a bound two-body system, the time it takes to go around once (the period) depends on the semi-major axis and the central body's gravitational parameter. The standard way to determine the period from the semi-major axis is Kepler's third law, written as P = 2π sqrt(a^3/μ), where μ = GM of the primary. This shows the period grows with the 3/2 power of the semi-major axis and directly uses a.

The vis-viva equation, v^2 = μ(2/r − 1/a), describes the speed at a specific point along the orbit given a and μ. It is excellent for finding instantaneous velocity but does not directly provide the orbital period from the semi-major axis. Newton's law underpins these relations and can derive them, but the straightforward, commonly used method to get P from a is Kepler's law. Hohmann transfer formulas relate to changing orbits, not the basic P–a relationship.