I want to know if I got this question right on my physics test

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The discussion revolves around calculating the centripetal acceleration of a shuttle in orbit 400 km above Earth's surface, with a 90-minute orbital period. The user correctly converted Earth’s radius and the orbital time into appropriate units and calculated the orbital speed as approximately 7900 m/s. Using the centripetal acceleration formula, they found the acceleration to be about 9.2 m/s², which is equivalent to 0.92 times the acceleration due to gravity (g). The user expresses uncertainty about their test answer, indicating it was significantly different from this calculation. They hope to receive extra credit for their efforts in redoing the problem.
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Homework Statement



A shuttle is in orbit 400km above the Earths surface, and circles it every 90 minutes. Find the centrip. acceleration and find it in terms of g. (He says for sake of ease, assume gravity = 10 m/s^2)

Earth radius = 6400 km

Homework Equations



a_{c}=\frac{v^2}{r}, v=\frac{2{\pi}r}{t}

The Attempt at a Solution



First I converted everything to meters and seconds:

6400 km = 6400000m, 90 minutes = 5400 seconds

v=\frac{2{\pi}r}{t}
v=\frac{2{\pi}(6400000+400000)}{5400}
v=7900\frac{m}{s}

a_{c}=\frac{v^2}{r}
a_{c}=\frac{7900^2}{6800000}
a_{c}=\frac{6.3{\cdot}10^7}{6800000}
a_{c}=9.2\frac{m}{s^2}

= .92g's
 
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Looks right, but I am not the one grading it.
 
damn, because i re did the question when posting it on this forum, but i remember that my answer on the test was nothign close to that

i hope i can get some extra credit.
 
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