Commit 3bab5ab2 authored by s-jdoyle4's avatar s-jdoyle4
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Question 20 from chapter 1

parent c8fd0bf4
For G to be converted into units of mass of earth, length unit of mean radius Earth-Sun orbit and unit of year. G is 6.67e-11 m^3kg-1s-2, so we must multiply the constraint by the mass of earth in kilograms (5.97e24), divided by the meters in the length of the mean radius of Earth-Sun orbit cubed(1.5e12)^3, and multiply the seconds that are a year of orbit squared (3.16e7)^2. so G in these units is 1.18e-7(mean radius)^3*(mass of Earth)^-1*(years)^-2. To use these units with the Moon to find the force between the earth and the moon, we must divid the mass of the moon in kilograms by the mass of earth in kilograms to get the moon in units of earth's mass and divid the distance of the mean of the moon's orbit in meters by the mean radius of Earth-Sun in meters to get it in the units of mean radius. So Mass of moon is 1.23e-2 earth's mass and distance of moon from earth is 2.57e-4 mean radius orbit of Earth-Sun and put on the equation (G*Mearth*Mmoon)/d^2 is 2.20e-2 earth's mass times Earth Sun mean orbit radius per a year squared. For force between the earth and Sun in these units we convert mass of sun from kilograms to units of earth's masses which is 3.33e5 earth's mass. So putting it in the equation (G*Mearth*Msun)/d^2 where d^2 = 1 earth mean orbit radius squared in these case, which is .039 earth's mass times Earth Sun mean orbit radius per a year squared.
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