At new moon the earth moon and sun are in a line find the...

At new moon, the Earth, Moon and Sun are in a line. Find the direction and magnitude of the net gravitational force exerted on a) the Earth, b) the Moon, and c) the Sun. What is the direction of the gravitational force exerted by the sun on the earth? What is the direction of the gravitational force exerted by the moon on the earth? What is the direction of the gravitational force exerted by the sun on the moon? What is the direction of the gravitational force exerted by the earth on the moon? What is the direction of the gravitational force exerted by the earth on the sun? What is the direction of the gravitational force exerted by the moon on the sun?

Transcript

00:01 During a new moon, the positions of the sun, moon, and earth are as shown.

00:06 Here on the right, i've also written the masses of the sun, ms, the moon, mm, and earth, m -e.

00:14 As well as the distances between the moon and earth, rme, and between the sun and earth, r -s -e.

00:23 The problem wants us to find the gravitational force exerted on the earth, the moon, and the sun, separately, in the system.

00:31 So first, let's look at the force on the earth.

00:38 We can write that as f .e.

00:42 And since it wants the direction too, we'll go ahead and write it as a vector.

00:48 F .e, the force on the earth, will be equal to force on the earth by the sun plus the force on the earth by the moon.

01:01 Now recall newton's gravitational law, fg is equal to big g, times m1 m2 over r squared and here the subscript g i will replace with 1 2 to show that it's the force on 1 by 2 so here we can go ahead and plug this formula back into the red equation g is or it's equal to g times m s over r e s or s or s or s since the distances are the same and here the force on the earth from the sun is pointing in the negative x direction where let's go ahead and call this direction x so it'll be a negative sign in the x direction plus g m e m over r m squared and this will be in the negative direction as well and remember that g is equal to 6 .67 times 10 to the minus 11 newtons squared over kilograms squared.

02:52 So here this would give us a force on the earth.

03:00 If we plug in all the numbers, it will be two negative x components and that gives us negative 3 .64 times 10 to the 22 neutrons in the x direction.

03:15 So that is the force on the earth.

03:19 Similarly for force on the moon we will have the force on the moon by the sun and the force on the earth i mean the moon from the earth and this will be equal to g and from the sun it will be the negative direction because the sun is pulling the moon in the negative x direction negative g m m s over rms here i'll go ahead and leave it like that for now the moon is, or the earth is pulling the moon in the positive x direction.

04:12 So be a positive g m, m, m, e over rme squared in the x direction.

04:23 And here, rms, rms can be written as rse, so the distance between the sun and the earth, subtract rme, the distance between the distance between the moon in the earth to get this distance right here which is rms...

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