Practice question
Question
A planet moves in an elliptical orbit around the Sun with a semi-major axis of 2.25×1011m. If its orbital period is 2 years, what is the mass of the Sun? (Take G\=6.67×10−11N m2/kg2, 1year\=3.156×107s)
Explanation
Using Kepler’s third law: T2 = 4π2GMsa3. Rearrange for Ms: Ms = 4π2a3GT2. T = 2×3.156×107 = 6.312×107s. a = 2.25×1011m. T2 = (6.312×107)2 = 3.984×1015s2. a3 = (2.25×1011)3 = 1.139×1033m3. Ms = 4×(3.14)2×1.139×10336.67×10−11×3.984×1015. Ms = 4.49×10342.657×105≈1.69×1030kg.