When the earth, moon, and sun form a right triangle, with the moon located at the right angle, the moon is in its third quarter phase. Find the magnitude and direction of the net force exerted on the moon. Give the direction relative to the line connecting the moon and the sun.
Please show all your work. 10 points to best answer.
Moon mass: 7.3477e22 kg
Earth mass: 5.9736e24 kg
Sun mass: 1.9891e30 kg
Earth to Moon distance: 3.84405e8 m
Moon to Sun distance: 1.50e11 m
Gravitational Constant = G = 6.67428e-11 m^3 kg^-1s^-2
The force of gravity: F = G* M*m/(r^2)
F(moon-sun) = 6.67428e-11 * 1.9891e30 * 7.3477e22 / (1.50e11)^2
F = 4.335e20 N
F(moon-earth) = 6.67428e-11 * 5.9736e24 * 7.3477e22 / (3.84405e8)^2
F = 1.9825e20 N
Converting to polar, we’ve got a magnitude of sqrt(f^2 + F^2) = 4.7668e20 N in the direction tan-1 (f/F) = 24.576 degrees earthward from the sun.
On the century when Newton lived, everybody believed there was one set of laws for objects here on earth, and a different set of laws for celestial bodies. Newton came to understand that his law of gravitation applied in both domains, therefore the word universal was added to the name, to emphasize this aspect.
F = 3.58×10^22
Direction = 0.147