1) The moon has a mass of 7.4 * 1022 kg and completes an orbit of radius 3.8 * 108 m about every 28 days. The Earth has a mass of 6 * 1024 kg and completes an orbit of radius 1.5 * 1011 m every year. What is the speed of the Moon in its orbit? Answer in units of m/s.

2) What is the kinetic energy of the Moon in orbit?

Answer in units of J.

3. What is the kinetic energy of the Earth? Answer in units of J.

What is the speed of the Moon in its orbit? Answer in units of m / s.

By definition we have that the speed in a circular movement is given by:

v = w * r

We then have to replace the values:

v = ((2 * pi) / (28 * (24/1) * (3600/1))) * (3.8 * 10 ^ 8)

v = 986.94 m / s

2) What is the kinetic energy of the Moon in orbit? Answer in units of J.

By definition, the kinetic energy is given by:

K = (1/2) * (m) * (V ^ 2)

Where,

m: mass

V: speed

Substituting the values we have:

K = (1/2) * (7.4 * 10 ^ 22) * ((986.94) ^ 2)

K = 3.60E + 28 J

3. What is the kinetic energy of the Earth? Answer in units of J.

First we must find the speed of the earth:

v = ((2 * pi) / ((1) * (365/1) * (24/1) * (3600/1))) * (1.5 * 10 ^ 11)

v = 29886 m / s

By definition, the kinetic energy is given by:

K = (1/2) * (m) * (V ^ 2)

Where,

m: mass

V: speed

Substituting the values we have:

K = (1/2) * (6 * 10 ^ 24) * ((29886) ^ 2)

K = 2.67E + 33 J

Mass of the moon Mm = 7.4 Ă - 10^22 kg

Moon orbital radius Rm = 3.8 Ă - 10^8 m

Time Tm = 28 days = 2.419 x 10^6

Mass of the Earth Me = 6 Ă - 10^24 kg

Earth orbital radius Re = 1.5 Ă - 10^11 m

Time Te = 365 days = 3.154 x 10^7

Length of Moon orbit Lm = 2 x pi x Rm = 2 x 3.14 x 3.8 Ă - 10^8 m = 23.86 x

10^8 m

Moon orbital velocity Vm = Lm / Tm = 23.86 x 10^8 m / 2.419 x 10^6 = 986.5 m/s

Kinetic Energy of the Moon = 1/2 x Mm x Vm^2 = 0.5 x 7.4 Ă - 10^22 x 986.5^2

Kinetic Energy of the Moon = 36 x 10^27 J

Length of earth orbit Le = 2 x pi x Re = 2 x 3.14 x 1.5 Ă - 10^11 = 9.42 x 10^11 m

Earth orbital Velocity Ve = Lm / Tm = 9.42 x 10^11 / 3.154 x 10^7 = 29866 m/s

Kinetic Energy of the Earth = 1/2 x Me x Ve^2 = 0.5 x 6 Ă - 10^24 x 29866^2

Kinetic Energy of the Earth = 26.76 x 10^32 J