(a) Calculate the magnitude of the angular momentum of the earth ...

Question

(a) Calculate the magnitude of the angular momentum of the earth in a circular orbit around the sun. Is it reasonable to model it as a particle? Consult Appendix E and the astronomical data in Appendix F

Accepted Answer

Hey everyone, welcome back in this video. We're asked when calculating mars angular momentum and around orbit around the sun, is it reasonable to consider it as a point mass? Okay, so is it reasonable to consider it a point mass. And were given this information about mars case were given the mass of mars the radius of mars and the radius of its orbit. Alright, so let's first look at the answers and kind of see what it is that we're trying to look at what we're trying to compare. Can we see that we have a comparison between the radius of the orbit and the radius of Mars. Okay, so the radius of the orbit we're given is 2.28 times 10 to the m. Okay. In the radius of the of Mars the planet itself is 3.39 times 10 to the six m. Okay, so those are quite a bit different. We're talking 10 to the 11 with the radius of the orbit. 10 to the six with the radius of Mars. Okay, so the radius of the orbit is going to be much greater than the radius of Mars. Okay, so we're looking at these answers. The first one says the radius of orbit is much greater, yep, radius of orbit much greater. Yet this is saying they're nearly equal. So we know. Okay. No it's not c it's not D because the radius is are not nearly equal and then e and f are telling us the radius of mars is greater than the radius of orbit. Well, that's not true. Right. The radius of the orbit is greater than the radius of mars. So we can already get rid of those answers. Now, we're down to A or B. Okay. So we found that the orbit the radius of the orbit is much greater than the radius of mars. But does that allow us to consider it a point? Us? Let's consider how much bigger. Okay, so we've determined that the radius of the orbit is much bigger than the radius of mars. By how much? Well, let's take the radius of the orbit. The ratio between the two the radius of the orbit divided by the radius of Mars. So 2.28 times 10 to the 11 m Divided by 3.39 times 10 to the six m. And that's gonna give us approximately 67257. Okay, so it's approximately 67,257 times bigger the radius of the orbit. Okay. That's a lot bigger. Now, when we're calculating the angular momentum, we're asking whether it matters when we're calculating angular momentum. Okay, We're calculating angular momentum. We're gonna need the moment of inertia and the moment of inertia. That's where that point mass is going to come in. Okay. If we're looking at the moment of inertia, we're considering the radius. Now. If we're considering the radius and we don't want to take it as a point mass. We're not taking mars as a point mass then the radius will have to consider will be the radius of MArs plus the orbital radius. Okay, so that will be the total distance from the middle to the access that we're rotating on. Okay. So we would have to consider our orbit plus our mars. Okay, well if we're adding these and the radius of the orbit is 67, times bigger then the radius of Mars won't contribute. Okay. Until around the sixth significant. Did you? Hm Alright, well it's not going to contribute to the six significant digit. And while we're doing physics questions like this we're using three significant digits in our answer. Okay, so it's not going to impact that calculation or the result of that calculation. Okay. It's the inclusion is going to be negligible. So it is indeed reasonable to assume that it's a point mass. So we're going to have a Yes. It's reasonable to assume that it's a point mass. The radio orbit is going to be much for the orbit radius story is going to be much greater than the radius of MArs. Thanks everyone for watching. See you in the next one

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