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Anderson Video - Difference Between the Sun and Earth's Gravity

Professor Anderson
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 >> Hello class. Professor Anderson here. Let's take a look at an interesting problem. Let's say that you are standing on the earth and you are looking up at the sun. So here is the earth and here is the sun. And you're standing here on the earth and the sun is directly above you, it is high noon. So gravity acts between all objects in the universe that have mass. And so there is a force on you due to the earth. And we will call that F sub earth. But there is of course another force on you, which is due to the sun. The sun is pulling on you, just like it's pulling on the earth, so forth. So there is a force on you due to the sun. And let's see if we can calculate the ratio of the force due to the sun, divided by the force due to the earth. Okay. What are gravitational forces? Well, Newton told us that the force -- let's just do one at a time. The force is equal to GMn over R squared. So the force due to the sun on you is G, mass of the sun times your mass, divided by the distance squared. But that distance is between you and the sun. And so, that is roughly the same as between the sun and the earth. And so we will call that RSE. And this is the distance from the sun to the earth. Okay. What about the force on the earth? Well, it's the same equation. G mass of the earth this time. Little m over how far you are from the center of the earth. And that's what we just call the radius of the earth. We're going to square that. Okay. And so now we can do the ratio. FS over FE equals GM sub S M over RSE squared. All over G mass of the earth, little m over RE squared. And so a few things cancel out here. The big G cancels out. The little m cancels out. And we can rewrite this as the following. Mass of the sun over mass of the earth, times R sub E over R sub SE quantity squared. And those numbers we can look up. So the radius of the earth is what? It is 6.37 times 10 to the 6th, meters. We are going to divide that by the distance from the sun to the earth, which is 1.5 times 10 to the 11 meters. Okay. And now we square that. And we multiply by the mass of the sun, which is 1.99 times 10 to the 30 kilograms. And, we divide by the mass of the earth, which is 5.98 times 10 to the 24 kilograms. And when you run all those numbers you get, like you might expect, a pretty small number. 6 times 10 to the minus 4. So, is the sun pulling up on you? Yeah, it is a little bit. But much, much less than the earth is pulling down on you and that's why we stay on the surface of the earth. Alright, hopefully that's clear. If not, come see me at my office. Cheers.