Motion of a satellite: orbital velocity, time period and energy
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See all →- The minimum energy required to launch a satellite of mass m from the surface of earth of mass M and radius R in a circular orbit at an altitude of 2R from the surface of the earth is: Answer: 2. 5GmM/6R Key idea: The minimum energy is the difference between the total energy in the orbit and the total energy at the surface.... 1
- A satellite is orbiting just above the surface of the earth with period T. If d is the density of the earth and G is the universal constant of gravitation, the quantity 3π/Gd represents : Answer: 3. T² For a satellite just above the surface, r=R and T=2π√(R³/GM) , so T²=4π²R³/GM . With M=4/3π R³d : T²=4π²R³/G·4/3π R³d=3π/Gd .... 1
- A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g_0, the value of acceleration due to gravity at the earth's surface, is Answer: 1. -mg₀R²/2(R+h) For a satellite in orbit, total energy is half of its (negative) potential energy: E=-GMm/2(R+h) . Use g₀=GM/R² , s... 1