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# Gravitation (part 2)

## Video transcript

welcome back so I was trying to rush and and finish a problem in the last two minutes the video and I realized that's just bad teaching because I end up rushing so this was a problem we were going to work on and you'll see a lot of these when they just wanted to become familiar with you know the variables in the in the gravity in the Newton's law of gravitation so I said that there's two planets one is earth now I have time to draw things so that's earth and then there's small earth and small earth will help me but I'll just call it the small planet done this we don't get confused it's green showing that there's probably life on that planet let's say it has half the radius and half the mass so if you think about it's probably a lot denser than Earth and that's that's a good problem to think about how much denser is it right because if you have half the radius your volume is much more than it's much less than 1/2 but I don't want to go into that now that's something for you to think about but my question is what fraction if I'm standing on the surface of this so the same person so Sal if I'm on earth what fraction is the pull when I'm on this small green planet so what is the pull on me on earth well it's just going to be so the my weight on earth the force on earth is going to be equal to the gravitational constant times my mass mass of well I already use so mass of me so M sub M times the mass of Earth divided by what we learned in the last video divided by the distance between me in the center of the mass of Earth really my center of mass in the center mass of Earth that's essentially just you know but this is between the surface of the earth and I'd like to think that I'm not short but it's negligible between my center of mass and the surface so we'll just consider the radius of the earth so we divided by the radius of the earth squared so what's using these same variables what's going to be the force on on this other planet so the force on the other planet the screen plant and I'll do it in green force on and we're calling it the small planet it equals what it equals the gravitational constant again and my mass doesn't change when I go from one planet to another right its mass now is what we the mass of this it's we would write an M sub s here right this is the small planet and we write we wrote right here that's half the mass of Earth so I'll just write that so it's 1/2 the mass of Earth and what's its radius what's the radius now I could just write the radius of the small planet squared but I'll say well we know it's 1/2 the radius of Earth so let's put that in there so 1/2 the radius of Earth we have to square it let's see what this simplifies to this equals so we have a we can take this 1/2 here 1/2 g mass of me times mass of earth over what's 1/2 squared it's 1/4 over 1/4 radius of Earth squared and what's 1/2 divided by 1/4 well 1/4 goes into 1/2 2 times right or another way you can think about it is if you have a fraction in the denominator when you put in the numerator you flip it and it becomes 4 so 4 times 1/2 is 2 either way it's just math so the force on this small planet is going to be equal to 1/2 divided by 1/4 is 2 times G mass of me times mass of Earth divided by the radius of Earth squared and if we look up here this is the same thing as this right it's identical so we know that the force that applied to me when I'm the surface of the small planet is actually 2 times the force applied on earth when I go to earth and that's something interesting to think about because you might have said initially wow you know gravity the mass of the object matters a lot in gravity the more mass of the object the more it's going to pull on me but I'm what we see here is that actually no when I'm on the surface of this smaller planet it's pulling even harder on me and and why is that well because I'm actually closer to its center of mass and as we talked about earlier in this video this this object is probably a lot denser you can say it's only it's half the mass but it's much less than half of the volume right because the volume is with the cube of the radius and all of that what I don't want to confuse you but this is just something to think about so not only does the mass matter but the radius matters a lot we and the radius is actually the square so it actually matters even more so that's that's a something that's that's pretty interesting to think about and these are actually very common problems when they just you know they want to tell you oh you go to a planet that is 2 times the mass of another planet etc etc what is the you know what is the difference in force between the two and one thing I want you to realize actually before I finish this video since I do have some extra time when we think about gravity especially with planets and all of that you always feel like oh it's earth pulling on me you always feel like let's say that this is the earth and the earth is huge and this is you know let's say this is a tiny spaceship right here you know and it's it's traveling you always think that earth is pulling on the spaceship right the gravitational force of Earth but actually turns out you know we when we looked at the formula it's a formula symmetric it's not nearly saying one is pulling on the other they're actually saying this is the force between the two objects they're attracted to each other so if the earth is pulling on me with the force of I don't know would if the forces if the earth is pulling on me with the force of 500 Newtons it actually turns out that I am pulling on the earth with an equal and opposite force of 5 Newtons we're pulling towards each other it just feels like the earth is at least from my point of view that the earth is pulling to me and we're actually both being pulled towards the combined center of mass so in this situation say the earth is pulling on this spaceship with the force of oh I don't know I I'm I'm making up numbers now but let's say it's a million Newton's 1 million Newtons it actually turns out that the spaceship will be pulling on the earth with the same force of 1 million Newtons and they're both going to be moved to their center of the combined system center of mass and the combined system center of mass since the earth is so much more massive is going to be very close to Earth's center of mass it's probably going to be heck very close to its center mask and be like right there right so in this situation Earth won't be doing a lot of moving but it will be pulled in the direction of the spaceship and the spaceship will try to go to Earth's center of mass but at some point probably the atmosphere or the rock that it runs into it won't be able to to go much further and it might crash right around there but anyway I want to just give you the sense that it's not necessarily one object just pulling on the other they're pulling towards each other - their combined center of masses and it would make a lot more sense if you know if we you know if they had just two people floating in space they actually would have some gravity towards each other it's almost a little romantic they would they would float to each other and actually you could figure it out on the you know the the I don't have the time to do it but you could use this formula and figure out that use the constant and you can figure out well what is the gravitational attraction between two people and what you'll see is is that between two people floating in space there are other forms of attraction that are probably stronger than than their their gravitational attraction anyway I'll let you ponder that and I will see you in the next video