Question

What is the Specific Mechanical Energy of the moon's orbit about the Earth? (Please provide a numerical answer to three decimal places and in units of km²/s²)

Here is some information that you might, or might not, need to solve this problem:

1. The mass of the moon is 7.348 × 10²² kg
2. The mass of the Earth is 5.972 × 10²⁴ kg
3. The mass of the Sun is 1.989 × 10³⁰ kg
4. The semi-major axis of the moon in its orbit about the Earth is 3.844 x 10⁵ km
5. The semi-major axis of the Earth in its orbit about the Sun is 1.496 x 10⁸ km
6. The Sun’s gravitational parameter is 1.327 x 10¹¹ km³/s²
7. The Earth’s gravitational parameter is 3.986 x 10⁵ km³/s²
8. The moon’s gravitational parameter is 4.905 × 10³ km³/s²

Answer 1