Physics: In this problem, you will calculate the location of the center of mass for the earth-moon system, and then you will calculate the center of mass of the earth-moon-sun system. the mass of the moon is 7.35×1022 kg , the mass of the earth is 6.00×1024 kg , and the mass of the sun is 2.00×1030 kg . the distance between the moon and the earth is 3.80×105 km . the distance between the earth and the sun is 1.50×108 km .

can somebody give me the answer so i can graduate...

In this problem, you will calculate the location

supiine1405

09.01.2022

Assuming that the earth is the center of all coordinates. The center of mass of the earth will be located at the coordinate x_1 = 0

To calculate the center of mass of the Earth-moon we require to proceed to the calculations given by,

$X_{e-m} = \frac{m_1x_1+m_2x_2}{m_1+m_2}$

Where

m_1 = Mass of earth

x_1 = Distance to center of mass for earth

m_2 = mass of moon

x_2 = Distance from moon to earth (to center of mass)

Replacing the values we have

$X_{e-m} = \frac{(6*10^{24})(0)+(7.35*10^{22})(3.8*10^5)}{6*10^{24}+0.0735*10^{24}}$

$X_{e-m} = \frac{27.93*10^{27}}{6.07*10^{24}}$

$X_{e-m} = 4.599*10^3km$

We extrapolate this procedure to the sun, but now including the three bodies, in this way

$X_{e-m-s}=\frac{(m_1+m_2)X_{e-m}+m_3x_3}{m_1+m_2+m_3}$

$X_{e-m-s}=\frac{(6.07*10^{24})(4.599*10^3)+(2*10^{30})(1.5*10^8)}{6.07*10^{24}+2*10^{30}}$

$X_{e-m-s}= 1.5*10^8km$

So we have the two center of mass:

System Earth-Moon equal to 4.599*10^3 km

System Earth-Moon-Sun equal to 1.5*10^8 km

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