Calculate the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth when the two forces are in direct competition, that is, when the Sun, Moon and Earth are aligned with the Moon between the Sun and the Earth. This alignment corresponds to a solar eclipse.) Does the orbit of the Moon ever actually curve away from the Sun, toward the Earth? (Please give your answer to three significant figures.)
I used G m1 m2/r^2 to get the forces, for the force between the Earth and the moon I did:
((6.67e-11)(5.97e24)(7.35e22))/(1.737e6 - 6.37e6)^2
and I got 1.36e24 N
For the force between the Sun and the Moon, I used the distance from earth to the sun and substracted it from the distance between moon to earth.
((1.737e6 - 6.37e6)- (6.96e8 -6.37e6))=6.95e8 m
and then for the moon to sun force I computed:
((6.67e-11)(7.35e22)(1.9891e30))/(1.737e6 - 6.37e6)^2
and I got 1.40e34 N...
Does these look right?
Physics (please check!!!) - drwls, Friday, April 29, 2011 at 1:42am
I don't understand how you are coming up with your r values. They should be center-to-center. You seem to be subtracting radii of the bodies themselves, to get a surface-to-surface distance.
For the sun-moon distance in a solar eclipse configuration, subtract the earth-moon distance from the earth-sun distance. You say it the other way around, but since it gets squyared, it doesn't matter.
The answer to your last question is "yes". The moon moves in and out compared to the orbit of the earth around the sun, sometimes moving away from the sun. Imagine a circle with 12 waves in it, in and out.
I don't get what I have to do... Do I have to add the radii instead??
To calculate the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth, you should use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (6.67e-11 N m^2/kg^2), m1 and m2 are the masses of the two objects, and r is the distance between their centers of mass.
For the force between the Earth and the Moon, you should use the distance between their centers of mass. Let's consider the average distance between the Earth and the Moon, which is about 384,400 km (1.737e6 m). The mass of the Earth is 5.97e24 kg and the mass of the Moon is 7.35e22 kg. Plugging these values into the formula, we have:
F_earth-moon = (6.67e-11 N m^2/kg^2) * (5.97e24 kg * 7.35e22 kg) / (1.737e6 m)^2
≈ 1.98e20 N
So, the magnitude of the gravitational force between the Earth and the Moon is approximately 1.98e20 N.
To calculate the force between the Sun and the Moon, you should consider the distance between their centers of mass when the Sun, Moon, and Earth are aligned. In this case, the distance between the Earth and the Moon becomes the distance between the Moon and the Sun, since the Moon is between the Sun and the Earth. The average distance between the Earth and the Sun is about 149.6 million km (1.496e11 m). Plugging these values into the formula, we have:
F_sun-moon = (6.67e-11 N m^2/kg^2) * (1.9891e30 kg * 7.35e22 kg) / (1.496e11 m)^2
≈ 1.04e22 N
So, the magnitude of the gravitational force between the Sun and the Moon is approximately 1.04e22 N.
Therefore, the magnitudes of the gravitational forces exerted on the Moon by the Sun and by the Earth when they are in direct competition (during a solar eclipse) are approximately 1.04e22 N and 1.98e20 N, respectively.
Regarding your question about the Moon's orbit, it does not always curve away from the Sun. The Moon's orbit around the Earth is not perfectly circular, so its distance from the Sun and the Earth varies. Sometimes, the Moon moves closer to the Sun and farther away from the Earth, and other times, it moves closer to the Earth and farther away from the Sun. It follows an elliptical path, resulting in a changing distance from both the Sun and the Earth.