During a lunar eclipse, the moon, earth, and sun all lie on the same line, with

Question

During a lunar eclipse, the moon, earth, and sun all lie on the same line, with the earth between the moon and the sun.  Calculate

a. the net force exerted on earth by the moon and the sun

b. the average velocity with which the moon orbits the earth

c. the centripetal acceleration of the moon

Use this information:  mass of the sun is 1.99x10^30kg, mass of the earth is 5.98x10^24kg, and mass of the moon is 7.35x10^22kg

Also:  radius of the sun is 6.96x10^5km, r of earth is 6.38x10^3km, r of moon is 1.74x10^3km

And:  earth-sun distance is 149.6x10^6km

earth-moon distance is 384x10^3km

I think where i went wrong with this is I forgot to add the radii in with the distance but Im not sure.  Please show all work!

Explanation / Answer

m = mass of moon = 7.36 x 10^22kg

M = mass of Earth = 5.98 x 10^24kg

M' = mass of Sun = 1.99 x 10^30kg

r = distance from Earth to moon = 3.84 x 10^8 m

R = distance from Earth to Sun = 1.496 x 10^11 m

G = Newton's gravitational constant = 6.67 x 10^-11

F = gravitational force = G*m1*m2 / r^2
(in general)



So now we solve:

F = G*M'*m / (R-r)^2

= (6.67x10^-11)*(1.99x10^30kg)*(7.36x10^22

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