Question

A geosynchronous satellite is one that stays above the same point on the Earth, which is possible only if it is above a point on the equator. a) Starting from Newton's law of universal gravitation, show that for a small object of mass m in a circular orbit of radius r with a large mass M in the center (M >> m), the speed v of the small mass is v = √(GM/r), and the orbital period is T^2 = 4π^2r^3/GM. b) Determine the height above Earth's surface a geosynchronous satellite must orbit. c) Determine the speed of such a satellite. Mass of Earth mE = 5.97 × 10^24 kg, radius of Earth RE = 6.37 × 10^6 m, mass of the satellite msat = 200 kg, and G = 6.67 × 10^-11 N∙m^2/kg^2.

          A geosynchronous satellite is one that stays above the same point on the Earth, which is possible only if it is above a point on the equator.

a) Starting from Newton's law of universal gravitation, show that for a small object of mass m in a circular orbit of radius r with a large mass M in the center (M >> m), the speed v of the small mass is v = √(GM/r), and the orbital period is T^2 = 4π^2r^3/GM.

b) Determine the height above Earth's surface a geosynchronous satellite must orbit.

c) Determine the speed of such a satellite.

Mass of Earth mE = 5.97 × 10^24 kg, radius of Earth RE = 6.37 × 10^6 m, mass of the satellite msat = 200 kg, and G = 6.67 × 10^-11 N∙m^2/kg^2.

Added by Don V.

Question

Please give Ace some feedback