Orbital Radius and Period: Doubling the Orbit

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To double the orbital period of a satellite, the orbital radius must be increased by a factor of approximately 1.59. The calculation used the formula T1/T2 = (r1/r2)^(3/2), leading to r1/r2 = (T1/T2)^(2/3). Substituting T1/T2 = 2 results in 2^(2/3) = 1.59. The solution appears to be correct based on the provided formulas and values. Understanding this relationship is crucial for satellite mechanics and orbital dynamics.
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Homework Statement


A satellite is orbiting above the earth. By what factor must the orbital radius be changed in order to double the period of the orbit? (Mearth = 5.98 x 1024kg, Rearth = 6.36x106m)

The Attempt at a Solution


i got 1.59 by T1/T2=(r1/r2)^3/2 so r1/r2=(T1/T2) ^2/3 so 2^2/3 =1.59 but i have no clue if i did that right
 
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Looks okay to me. :approve:
 

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