According to Kepler's third law, T is proportional to which power of the semi-major axis a when the central body's gravity parameter μ is constant?

Unlock all questions

This demo includes only 20 questions. Upgrade to access hundreds of questions, flashcards, exam simulations, and disable ads.

Full question bankExam simulationsFlashcards
From $24.99Unlock all

Prepare effectively for the STARS TAP Exam with flashcards and multiple choice questions, each featuring hints and explanations. Equip yourself to excel and reach new heights in your space training journey!

Multiple Choice

According to Kepler's third law, T is proportional to which power of the semi-major axis a when the central body's gravity parameter μ is constant?

Explanation:
The relation you’re testing is that the orbital period grows with the size of the orbit in a specific way: for a central body with constant gravity parameter μ, the period squared is proportional to the semi-major axis cubed. In formula form, T^2 = (4π^2/μ) a^3, which means T = 2π sqrt(a^3/μ). Since μ is fixed, T scales as a^(3/2). So larger orbits take longer, and the increase follows the 3/2 power, not linearly or more steeply. This is why doubling the semi-major axis makes the period increase by 2^(3/2) ≈ 2.83, not by a factor of 2 or 4.

The relation you’re testing is that the orbital period grows with the size of the orbit in a specific way: for a central body with constant gravity parameter μ, the period squared is proportional to the semi-major axis cubed. In formula form, T^2 = (4π^2/μ) a^3, which means T = 2π sqrt(a^3/μ). Since μ is fixed, T scales as a^(3/2). So larger orbits take longer, and the increase follows the 3/2 power, not linearly or more steeply. This is why doubling the semi-major axis makes the period increase by 2^(3/2) ≈ 2.83, not by a factor of 2 or 4.

More Multiple Choice Questions
Subscribe

Get the latest from Examzify

You can unsubscribe at any time. Read our privacy policy