Question

Find the radius RRR of the orbit of a geosynchronous satellite that circles the Earth. (Note that RRR is measured from the center of the Earth, not the surface of the Earth.) Use the following values if needed in this problem: The universal gravitational constant GGG is 6.67×10−11Nm2/kg26.67×10−11Nm2/kg2. The mass of the earth is 5.98×1024kg5.98×1024kg. The radius of the earth is 6.38×106m6.38×106m.

Answer 1

Answer:

The raduis of the geosynchronous orbit of the satellite around earth is 3.88×10^10m

Explanation:

The raduis of geosynchronous orbit of a satellite is given by:

R = Cuberoot(T^2GM)/4pi r^2

Given:

G = gravitational constant = 6.67×10^-11Nm^2

M = mass of earth = 5.98×10^24kg

r = radius of the earth = 6.38×10^6m

T = time period on the earth = 24hours

Changing hours to seconds = 24 ×60minutes ×60 seconds = 86,400seconds

Substituting into the equation

R = Cuberoot[ (86,400)^2 × (6.67×10^-11)×(5.98×10^24) / (4×3.142×(6.38×10^6)^2]

R = Cberoot [ (2.98×10^46)/(5.12×10^14)]

R = Cuberoot(5.82×10^31)

R = 3.88×10^10m