Question
ACT Practice Question:
The Earth orbits the Sun with an approximate period of 365 days.
What is the new orbital period if Earth's mass were suddenly to double?
(1 point)
Responses
258 days
258 days
365 days
365 days
516 days
516 days
730 days
730 days
182 days
The Earth orbits the Sun with an approximate period of 365 days.
What is the new orbital period if Earth's mass were suddenly to double?
(1 point)
Responses
258 days
258 days
365 days
365 days
516 days
516 days
730 days
730 days
182 days
Answers
GPT-5 mini
365 days.
Reason: By Kepler's third law for two bodies, T^2 ∝ 1/(M_sun + M_earth). Doubling Earth's mass changes M_sun + M_earth by a tiny amount (M_earth ≈ 3×10^-6 M_sun), so the period changes by only ~0.00055 days (≈48 seconds). Practically it remains 365 days.
Reason: By Kepler's third law for two bodies, T^2 ∝ 1/(M_sun + M_earth). Doubling Earth's mass changes M_sun + M_earth by a tiny amount (M_earth ≈ 3×10^-6 M_sun), so the period changes by only ~0.00055 days (≈48 seconds). Practically it remains 365 days.