What is the radius of a communications satellite’s orbital path that is in a uniform circular orbit around Earth and has a period of exactly 24.0 hours (86,400 seconds). (Measurement is from the center of Earth.)

What is the radius of a communications satellite’s orbital path that is in a uniform circular orbit around Earth and has a period of exactly 24.0 hours (86,400 seconds). (Measurement is from the center of Earth.) A. 6.5 × 10^4 m B. 3.8 × 10^5 m C. 4.2 × 10^7 m D. 9.5 × 10^7 m

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Vespertilio Vespertilio · Answer 2 · 2019-06-11T10:26:46+02:00

Answer:

42400 km

Explanation:

The time taken by a satellite to complete one revolution around the earth is called the time period of the satellite.

The time period for the satellite is given by

[tex]T = \frac{2\pi }{R}\times \sqrt{\frac{(R+h)^{3}}{g}}[/tex]

where, R be the radius of earth, h be the height of satellite from earth's surface and g be the acceleration due to gravity.

Substitute, 86400 s for T, 6400000 m for R and 9.8 m/s^2 for g , we get

[tex]86400 = \frac{2\pi }{6400000}\times \sqrt{\frac{(6400000+h)^{3}}{9.8}}[/tex]

h = 35954355.13 m

h = 36 x 10^3 km

Distance from the centre of earth is R + h = 6400 km + 36000 km = 42400 km .