When the earth moon and sun form a right triangle with the...

When the Earth, Moon, and Sun form a right triangle, with the Moon located at the right angle, as shown in the figure(Figure 1), the Moon is in its third-quarter phase. (The Earth is viewed here from above its North Pole.) Find the magnitude of the net force exerted on the Sun. Find the direction of the net force exerted on the Sun. Give the direction relative to the line connecting the Sun and the Moon.

Transcript

00:01 And this class, you basically look at the sun, earth, moon system, right? now, imagine you have a sign here, right? the sun is here, and the earth is circular like this.

00:11 Suppose this is an orbit of the earth, which i will, let's say, use a color to indicate.

00:18 We have a blue planet, right? somewhere here.

00:21 So that's our earth, right? now, so i will play it by e, that's earth.

00:26 Now, imagine we also have the moon.

00:28 The moon is denoted by a green circle, which is somewhere here.

00:33 Supposed it also orbits with, you know, the moon orbits with the earth, right? it's going like this.

00:39 So the moon will be somewhere here according to situations to that these three objects, these three objects were form a triangle, right? so the triangle will be something in this.

00:52 Let me try to plot triangle, something like this.

00:57 You will have a triangle, right? if you connect, join them, you will get a triangle, somewhere like this, right? and of course, you would also get this part.

01:09 So that's a triangle, and the moon is, so this is the moon, right? the moon is on the right, at the right angle, right? and of course, now you can work out the gravitational force exerted by the moon and earth on the sound, right? so first, the moon is going to attract the sign this way, and the earth is going to contract the sign this way and you add them together, right? the easiest way to do this is to decompose the gravitation force between the sun and earth in two components, right? let me do that this way.

01:57 So you have this part and you have also this part, right? so this component, it's perpendicular to the line between the moon and the sun, while this component is in the same direction as the force exerated by the moon, right? so this part and this part add together, right? so you can work out that easily because you know the distance, the distance between the, i mean, the radius of the earth's orbit, right? let that distance be, let's say i call it d, right? i don't know, d, maybe i call it r, right? and then obviously the gravitational force would be just the g and times the mass of the moon, right? i'll write it as m, moon, okay? m, that's the mass of the moon, and then multiply the mass of the sun like this, and then divided by r squared...

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