How long does it take for a satellite to go once around the earth, in minutes? U

Question

How long does it take for a satellite to go once around the earth, in minutes?
Use the fact that the Earth’s gravity Fgravity = GMm/r2 supplies the force to keep the satellite orbiting in a circle Fcircular = mv2/r.
Here M is the mass of the Earth M = 6 x 1024 kg and
G = 6.7 x 10-11 m3 /(kg-sec2).
If the satellite is in “low Earth orbit”, one or two hundred miles up, then the radius of the orbit is the radius of the Earth (a little less than 4000 miles) + the altitude of the orbit (say 200 miles), or r ~ 6.7 x 106 meters.
Also use the fact that the satellite’s speed is the distance once around the Earth (2pr) divided by the orbital period (i.e., the time).

Explanation / Answer

Period of the satellite T = 2 [ R 3 / GM] Where G = Gravitational constant                 = 6.67 x10 -11 N m 2 / kg 2              M = Mass of earth                  = 5.98 x 10 24 kg              R = Radius of orbit                 = 6.7 x 10 6 m Substitue values we get T = 2 ( 868.35 )                                         = 5456 s                                        = 5456 / 60 min                                        = 90.93 min

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