As discussed in class, the moon is receding from the Earth due to tides at a rate of ~4 cm/year. Let’s assume that rate has been constant throughout time (it wasn’t, but we can use it to illustrate some key points). Its current semi-major axis is 384,400 km. a) If the moon formed 4.5 billion years ago and has been receding from the Earth ever since, what was its original semi-major axis? What was its original orbital period? b) What would the apparent size of the Moon have been in the sky as viewed from Earth? That is, in Hmwk 2, you were told the diameter of the Moon spans about 0.5o when viewed from Earth today. What would it have been when the Moon first formed?
As discussed in class, the moon is receding from the Earth due to tides at a rate of ~4
cm/year. Let’s assume that rate has been constant throughout time (it wasn’t, but we
can use it to illustrate some key points). Its current semi-major axis is 384,400 km.
a) If the moon formed 4.5 billion years ago and has been receding from the Earth
ever since, what was its original semi-major axis? What was its original orbital period?
b) What would the apparent size of the Moon have been in the sky as viewed
from Earth? That is, in Hmwk 2, you were told the diameter of the Moon spans about
0.5o when viewed from Earth today. What would it have been when the Moon first
formed?
Reletive Numbers
Relevant Numbers
1 AU = 150,000,000 km = 1.5x108 km
Eccentricity of Earth’s Orbit: 0.0167
Radius of Earth: 6371 km
Mass of Earth: 5.96x1024 kg
Radius of the Moon: 1737 km
Mass of Moon: 7.34x1022 kg
Radius of Mars: 3390 km
Mass of Mars: 6.4x1023 kg
Radius of the Sun: R⦿=696,300 km
Mass of the Sun: M⦿=2x1030 kg
Gravitational Constant: G=6.67x10-11 m3/(kg s2)
Speed of light: c=3x108 m/s
Relevant Equations
Kepler’s 3rd Law:
P2 = (4π 2/GMcenter) a3
Here, Mcenter is the mass of the central body
around which things orbit, such as the Sun.
This is true if the orbiting body has a small
mass compared to the central body.
Newton’s Law of Universal Gravitation:
F = GMm/d2
Here, M is the mass of one body, m the mass
of another, G the universal Gravitational
Constant, and d the distance between the
centers of the two objects.
λmax=0.0029mK
T
TF=9
5TC+32
TK=TC+273
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