A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the speed of the satellite is 7.9 km/s, what is the centripetal acceleration?

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Q: A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the speed of the satellite is 7.9 km/s, what is the centripetal acceleration?

Solution: Centripetal acceleration a_c = v²/r = (7.9 km/s)² / (7000 km) = 0.00063 km/s² = 6.3 m/s².

Steps: 7

Step 1: Identify the formula for centripetal acceleration, which is a_c = v² / r.
Step 2: Note the values given: the speed (v) of the satellite is 7.9 km/s and the radius (r) of the orbit is 7000 km.
Step 3: Square the speed of the satellite: (7.9 km/s)² = 62.41 km²/s².
Step 4: Divide the squared speed by the radius: 62.41 km²/s² / 7000 km.
Step 5: Perform the division: 62.41 / 7000 = 0.0089142857 km/s².
Step 6: Convert the result from km/s² to m/s² by multiplying by 1000 (since 1 km = 1000 m): 0.0089142857 km/s² * 1000 = 8.9142857 m/s².
Step 7: Round the result to two decimal places: 8.91 m/s².

A satellite is in a circular orbit around the Earth. If the radius of the orbit is 7000 km and the speed of the satellite is 7.9 km/s, what is the centripetal acceleration?

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