orbiting a planet which has a sidereal rotation time of 16 hours, a surface radius of 6e6 m and surface gravitational acceleration of 10 (m/s)/s ?
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m w^2 R = GMm/R^2 = g m (R0/R)^2
so w^2 R = 10 (6*10^6 /R)^2
w^2 R^3 = 10 * 36 * 10 ^ 12
and w = 2* pi() /(16 * 60 * 60)
so R^3 = 10 * 36 * 10^12 /( 2* pi() /(16 * 60 * 60) )^2
R =( 10 * 36 * 10^12 /( 2* pi() /(16 * 60 * 60) )^2 )^(1/3)
= 31.2 * 10 ^ 6 m
so w^2 R = 10 (6*10^6 /R)^2
w^2 R^3 = 10 * 36 * 10 ^ 12
and w = 2* pi() /(16 * 60 * 60)
so R^3 = 10 * 36 * 10^12 /( 2* pi() /(16 * 60 * 60) )^2
R =( 10 * 36 * 10^12 /( 2* pi() /(16 * 60 * 60) )^2 )^(1/3)
= 31.2 * 10 ^ 6 m