Question

How much energy Δ???? would be required to move the Moon from its present orbit around Earth to a location that is twice as far away? Assume the Moon’s orbit around Earth is nearly circular and has a radius of 3.84×108 m. Δ

Answer 1

Answer:

$W = 1.9 \times 10^{28} J$

Explanation:

As we know that total energy of satellite is given as

$E = -\frac{GM_1M_2}{2r}$

now we know that work done to change the orbit is equal to change in the total energy of Earth - Moon system

so we know that

$W = E_f - E_i$

$W = -(\frac{GM_1M_2}{2r_2}) + (\frac{GM_1M_2}{2r_1})$

$W = \frac{GM_1M_2}{2}(\frac{1}{r_1} - \frac{1}{r_2})$

$W = \frac{(6.67 \times 10^{-11})(7.35 \times 10^{22})(5.98 \times 10^{24})}{2}(\frac{1}{3.84 \times 10^8} - \frac{1}{7.68 \times 10^8})$

$W = 1.9 \times 10^{28} J$