Find the centripetal acceleration of the space shuttle

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To find the centripetal acceleration of the space shuttle in orbit 400 km above Earth's surface, the correct radius should be the sum of Earth's radius (approximately 6371 km) and the altitude (400 km), totaling about 6771 km. The formula for centripetal acceleration is Ac = v²/r, where v is the orbital speed. The shuttle orbits the Earth approximately every 90 minutes, which requires converting this time into a speed in meters per second. The final calculated centripetal acceleration should be expressed in terms of g, with the expected result being around 0.9 g's. Accurate conversion and calculations are crucial for obtaining the correct answer.
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1. Suppose a space shuttle is in orbit 400 km from the Earth's surface, and circles the eart about once every 90 minutes. Find the centripetal acceleration of the space shuttle in its orbit. Express your answer in terms of g, the gravitational acceleration at the Earth's surface.



2. Ac=v2/r



3. I tried converting 400km/1.5 hr to km/h...then to m/s and divided by 90 min to find the centripetal acceleration, then divinding this answer by 9.8 to find the final answer in g's.

The answer is supposed to be .9 g's.

I have tried this probelm a million times, and I honestly think that my mistake is in converting 400km. I'm not sure though...
 
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You haven't used 400 km as the radius, have you? The radius is the distance to the center of the Earth, not to the surface. Recommend you show your actual calc if you need more help.
 

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