The time period of a satellite near Earth’s surface is 84 minutes. What is its time period at a height h\=RE? (RE\=6.4×1
T2 = k(RE+h)3, where k = 4π2GME. For h = 0, T0 = 84min, T02 = kRE3. For h = RE, r = 2RE, T2 = k(2RE)3 = 8kRE3. T = 8T0 = 2.828×84≈237min.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.