A satellite that goes around the earth once every 24 hours is called a geosynchronous satellite. If a geosynchronous satellite is in an equatorial orbit, its position appears stationary with respect to a ground station, and it is known as a geostationary satellite.
Find the radius R of the orbit of a geosynchronous satellite that circles the earth. (Note that R is measured from the center of the earth, not the surface.) You may use the following constants:
The universal gravitational constant G is 6.67×10−11Nm2/kg2.
The mass of the earth is 5.98×1024kg.
The mass of the satellite is 2.10×102kg.
The radius of the earth is 6.38×106m.
Give the orbital radius in meters to three significant digits.

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SidHussain SidHussain · Answer 1 · 2022-12-02T19:45:39+01:00

The radius of the orbit of a geosynchronous satellite that circles the Earth is calculated to be 4.23 x 10^7 m

As the given time period is 24 hours, we first convert it into seconds as follows;

24 x 3600 = 86,400 seconds

The formula for the time period of the satellite can be given as;

T = 2π √r³ ÷ GM

Here r represents the radius, M represents the mass of the Earth and G illustrates the universal gravitational constant.

86,400 = 2 × 3.14 √r³ ÷ (6.67×10^−11) (5.98×10^24)

1.89 × 10^8 = r³ ÷ (6.67×10^−11) (5.98×10^24)

r = 4.23 x 10^7 m

Therefore the radius of the orbit of a geosynchronous satellite is 4.23 x 10^7 m

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