USAAAO — 2025 First Round
Question 13
A recently observed exosolar system consists of a star, a planet, and the planet’s satellite. The satellite has a revolution period of 100 minutes around the planet, and the planet has a 90 day revolution period around the star. The satellite approaches the surface of the planet to a minimum height of 1000 km and recedes to a maximum height of 7000 km. The radius of the planet is 3000 km. If the ratio of the mass of the star to the mass of the planet is 1 × 10⁵, what is the semi-major axis of the planet’s revolution around the star? Assume that the mass of the satellite is much smaller than the mass of the planet.
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Source
USAAAO 2025 First Round, Question 13. Question text, choices, and answer were transcribed from the official USAAAO exam and solutions PDFs.