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 km^{2}/s^{2})

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

- The mass of the moon is 7.348 × 10
^{22}kg - The mass of the Earth is 5.972 × 10
^{24}kg - The mass of the Sun is 1.989 × 10
^{30}kg - The semi-major axis of the moon in its orbit about the Earth is
3.844 x 10
^{5}km - The semi-major axis of the Earth in its orbit about the Sun is
1.496 x 10
^{8}km - The Sun’s gravitational parameter is 1.327 x 10
^{11}km^{3}/s^{2} - The Earth’s gravitational parameter is 3.986 x 10
^{5}km^{3}/s^{2} - The moon’s gravitational parameter is 4.905 × 10
^{3}km^{3}/s^{2}

Answer #1

Given that the mass of the Earth is 5.972 X 1024 kg,
the mass of the Moon is 7.346 X 1022 kg, and the
distance, center of mass to center of mass is 3.85 X 105
km
What is the force of gravitational attraction between the
two?

An Earth satellite’s orbit has a period of 55.555 hours, and a
semilatus rectum of 72,254.4 km. What is the orbit’s
eccentricity?
Equations:
a = {(ra + rp)/2}
ra = a (1 + e)
rp = a (1 - e)
p = (b2/a) = a (1 – e2)
h = rpvp = rava
ε = - μ/(2a)
P = 2π√(a3/μ)
Use: Earth radius = 6378.1363 km
Gravitational parameter μ = 3.986012 X 105 km3/sec2

QUESTION 1
Part 1
Engineers wish to launch a satellite from the surface of the
Moon. What is the minimum speed the satellite must have to escape
the Moon’s gravity – that is, what is the escape velocity at the
surface of the Moon? The Moon has a mass of 7.3x10^22 kg and a
radius of 1.7x10^6 m.
a.
1700 m/s
b.
5.7x10^6 m/s
c.
It depends on the mass of the satellite.
d.
2400 m/s
Part 2
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