QuestionA 4025 kg spacecraft is in circular orbit around the Earth at an altitude of 256 km . Determine; a) the kinetic energy of the spacecraft b) the gravitational potential of the spacecraft $42.56 \times 10^{5} \mathrm{~m}$ c) the total orbital energy of the space craft d) the binding energy of the space craft e) the speed required for escape at this height f) the work required to move the spacecraft to a new orbit of altitude 628 km g) homework; pg WS \#'s 4, 5, 7, 8, \& 10

Studdy Solution
Calculate the work required to move the spacecraft to a new orbit of altitude 628 km.
6.1 Determine the new orbital radius $r'$: $$r' = \text{Earth's radius} + \text{new altitude} = 6371 \, \text{km} + 628 \, \text{km} = 6999 \, \text{km} = 6999000 \, \text{m}$$
6.2 Calculate the change in gravitational potential energy: $$\Delta U = \left(-\frac{GMm}{r'}\right) - \left(-\frac{GMm}{r}\right)$$
6.3 Calculate the work done $W$: $$W = \Delta U$$
Note: The homework part is not a calculation step and is not addressed here.