Determine the amount of work in joules that must be done on

Determine the amount of work (in joules) that must be done on a 95 kg payload to elevate it to a height of 991 km above the Earth\'s surface. Determine the amount of additional work that is required to put the payload into circular orbit at this elevation.

Solution

R_E+y = 6370 + 991 = 7.33 * 10⁶ m

W = U_f - U_i = G M_E m [1/R_E - 1/R_E+y]

= 6.67 * 10^-11 * 5.98 * 10²⁴ * 95 * [(1/6.37 * 10⁶) - (1/7.33 * 10⁶)]

= 7.79 * 10⁸ J

b) K = G M_E m / 2 (R_E+y)

= (6.67 * 10^-11 * 5.98 * 10²⁴ * 95) / (2 * 7.33 * 10⁶)

= 2.43 * 10⁹ J