A satellite orbits a planet at 4×107m from its center with a period of 8 hours. What is the planet’s mass? (G\=6.67×10−1
M = 4π2r3GT2. T = 8×3600 = 28800s, T2 = 8.2944×108s2. r3 = (4×107)3 = 6.4×1022m3. M = 4×(3.14)2×6.4×10226.67×10−11×8.2944×108. M = 2.523×10245.532×10−2≈4.56×1025kg. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 4.6 × 10²⁵ kg. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.
