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(II) The masses of the Earth and Moon are $5.98 \times 10^{24} \mathrm{kg}$ and $7.35 \times 10^{22} \mathrm{kg},$ respectively, and their centers are separated by $3.84 \times 10^{8} \mathrm{m}$ . (a) Where is the CM of this system located? (b) What can you say about the motion of the Earth-Moon system about the Sun, and of the Earth and Moon separately about the Sun?

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a) $4.66 \times 10^{6} m$b) It is this Earth-Mloon CM location that actually traces out the orbit as discussed in an earlier chapter. The Earth and Moon will orbit about this orbit path in (approximately) circular orbits. The motion of the Moon, for example, around the Sun would then be a sum of two motions:i) The motion of the Moon about the EarthMoon CM; andii) The motion of the EarthMoon CM about the Sun.To an external observer, the Moons motion would appear to be a small radius, higher frequency circular motion (motion about the EarthMoon CM) combined with a large radius, lower frequency circular motion (motion about the Sun). The Earths motion would be similar, but since the center of massof that Earth-Moon motion is inside the Earth, the Earth would be observed to wobble about that $\mathrm{CM} .$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

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Okay, so you're interrupting our problem. Somebody through here. So it gives us the masses of the earth and the moon and wants us to find the center of mass of the system and also the distance of their center. So the center of mass of the Earth moon system will be given by position here, massive, eager, plus the position of the moon massive over some of their masses. So if we want to find this relative to the center of the earth than done position of the earth will be zero. The position of the moon is the distance between them witches for 84 it's an eight. Promise comes Tim to the eight meters and the mass of the moon is 7.35 terms 10 22 kilograms. The total mass here is mass of the earth. Cost the massive. Okay, we got in. We get the center of mass of the system as 4.66 times 10 to 6 meters from the center of the earth. Now, the radius of the radius of earth is 6.38 times 10 to 6 meters, which means the center of mass of the Earth moon system this being the earth here and are moving over here center of mass is about here. Just still inside the earth in system are sitting inside the earth. Look it. So I was part of a now asked us to interpret this kind of and say What can we say about motion of the earth moon system about the sun? Well, that means if both of these are rotating around the sun all the way over here, we can see that the actual motion is the sum of two motions, right? Some of that object rotating around the earth, a really big radius plus at a very low frequency. Plus this emotion about the earth moon center of mass at a higher frequency. So what that means is that this is actually two motions that they're seeing to an extra hopes ever. Although from the Earth, it seems just like one motion. And now what can we say about the Earth moon separately in this stuff? Well, just looking at the Earth moon system, it appears like the sun is being roughly circle e circular. Just around that, and the earth since the center of mass is still within the earth's radius, that just looks like a little wobble about that point

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