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Setler79 [48]
3 years ago
11

A satellite orbits the earth a distance of 1.50 × 107 m above the planet's surface and takes 8.65 hours for each revolution abou

t the earth. The earth's radius is 6.38 × 106 m. The acceleration of this satellite is closest to___________.
Physics
1 answer:
kupik [55]3 years ago
6 0

Answer:

The acceleration of the satellite is 0.87 m/s^{2}

Explanation:

The acceleration in a circular motion is defined as:

a = \frac{v^{2}}{r}  (1)

Where a is the centripetal acceleration, v the velocity and r is the radius.

The equation of the orbital velocity is defined as

v = \frac{2 \pi r}{T} (2)

Where r is the radius and T is the period

For this particular case, the radius will be the sum of the high of the satellite (1.50x10^{7} m) and the Earth radius (6.38x10^{6} m) :

r = 1.50x10^{7} m+6.38x10^{6}m

r = 21.38x10^{6}m

Then, equation 2 can be used:

T = 8.65 hrs \cdot \frac{3600 s}{1hrs} ⇒ 31140 s

v = \frac{2 \pi (21.38x10^{6}m)}{31140s}

v = 4313 m/s

Finally equation 1 can be used:

a = \frac{(4313m/s)^{2}}{21.38x10^{6}m}    

a = 0.87 m/s^{2}

Hence, the acceleration of the satellite is 0.87 m/s^{2}

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