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A satellite orbits the earth at a distance of 1.50 × 10^{7} m above the planetʹs surface and takes 8.65 hours for each revolution about the
Question
A satellite orbits the earth at a distance of 1.50 × 10^{7} m above the planetʹs surface and takes 8.65 hours for each revolution about the earth. The earthʹs radius is 6.38 × 10^{6} m. The acceleration of this satellite is closest to
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2021-08-20T17:32:47+00:00
2021-08-20T17:32:47+00:00 1 Answers
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Answer:
a = 0.43 m/s²
Explanation:
First, we need to find the velocity of the satellite:
Velocity = V = Distance Covered/Time Taken
here,
Distance = 1 revolution = 2π(1.5 x 10⁷ m) = 9.43 x 10⁷ m
Time = (8.65 hours)(3600 s/1 hour) = 31140 s
Therefore,
V = (9.43 x 10⁷ m)/(31140 s)
V = 3028.26 m/s
Now, the acceleration of the satellite will be equal to the centripetal acceleration, with the center of circular motion as the center of earth:
a = V²/R
where,
R = 1.5 x 10⁷ m + 0.638 x 10⁷ m
R = 2.138 x 10⁷ m
Therefore,
a = (3028.26 m/s)²/(2.138 x 10⁷ m)
a = 0.43 m/s²