so we're talking about Newton's law of gravitation what Newton's law of gravitation tells us is that all objects in the universe attract one another so right here I have a Kleenex box and I have my remote to the projector is the kleenex box a mass yes is the remote a mass yes so what do we know about these two masses they are even though you can't see it or even feel it what do we know to be true about these two masses they're attracting each other all objects in the universe attract each other this is Newton's law of gravitation now there's an equation for it the equation for finding the gravitational we we refer to the the force of attraction between masses it is a gravitational force of attraction so notice the little subg right here Force gravitational uh it's equal to Big G which you have not seen this before don't confuse the Big G with the lowercase G lowercase G would be acceleration of gravity this big G is what we call the gravitational constant now I just want to draw your attention to something look at how small the gravitational constant is 6673 * 10 to the 11 so let's say we got two small objects just you know a 1 kg mass and a 1 kg Mass like you know here I have a 1 kg mass and a 1 kg Mass separated by 1 meter you're not going to notice the force of attraction because look when you plug into this equation the uh the gravitational constant is 2 3 4 5 6 7 8 9 10 6 6 73 Newton met squ over kilogram squared uh let's say that the first mass is 1 kilogram the next mass is another kilogram and they're separated by one meter is this going to give you a noticeable Force no and the reason is the gravitational constant is too small so in order to get a noticeable Force here in order for this force to be noticeable what has to be true about one of these masses not both of the masses just one of these Mass masses must be what incredibly large and am I talking like the size of my car large no am I talking like the size of my house large even bigger what type of large am I talking about like a planet like the Earth okay so let's say that the Earth is M1 and by the way we do know the mass of the Earth it's it be given let's say the Earth is one mass and then this Kleenex box is another Mass would there be a noticeable for force between the Earth and this Kleenex box let's just make sure let's just see ready yep there was a noticeable Force there as you all saw the kleenex box got pulled down to the Earth okay um okay a couple things so look over here in this equation for finding the gravitational force between two masses so I have a diagram here we have a small M1 so we're looking over here now we have a small M1 and a larger M2 um these masses will attract each other M1 is attracted to M2 and we'll label that as FG for a for gravitational force it's a gravitational force of attraction uh and then this is gravitational force so M1 is attracted to M2 and M2 is attracted to M1 but here's the catch M1 is smaller and M2 is larger will these two forces be the same or different how many of you say they'll be the same how many of you say they'll be different uh okay only about four people who says they're going to be the same yes who says they're going to be different no they're they're the same now in fact Newton hey Newton has another law for why this is true it's called Newton's Third Law remember what Newton's third law is every Force has a equal and opposite reaction force so this is a perfect example of that perfect example of this the small guy M1 exerts a force on M2 that's this Force right here M1 exerts a force on M2 and then what's M2 doing to M1 exerting a force back these guys are exerting a mutual force on each other they're mutually attracted to each other other it's just like you sitting right in this room look is the earth pulling you down yes Prine look up here the Earth is pulling you down so what else must be true you are pulling the Earth up those two forces are equal even though you're small and the Earth is Big the force that you exert on the earth is equal to the force that the Earth exerts on you every Force has an equal and opposite reaction force okay that's a very common question because kids look at this and they're like oh they start thinking the forces must be different because one is big and the other one's small okay another thing I want to point out here in this equation R is from Center to center right from the center this is going to be important in a minute from Center to center from the center of M1 to center of M2 all right now there are two applications for Newton's law of gravitation the two applications are first one finding the acceleration of gravity on or above a really large mass and look at the end of the day this is the equation that you're going to be using but guys do I want you to memorize that equation no what I would prefer is that you know how to figure it out which is what I'm going to show you right here it's very simple Okay who wants to be my volunteer I'm going to send you on a rocket way far away from the earth who want wants to be on a rocket way far away from the earth okay Reed Reed is going to be it was like that who was that guy the the Red Bull guy who jumped out of that balloon like set the record for a highest Skydive what was his name Rufus Felix Felix Felix okay so here's Felix guys Felix no sorry no it's Reed sorry Reed it's Reed here we go we got Reed and Reed you're going to be M2 because the Earth is bigger so we're going to call the Earth M1 now the important distance here the important distance is from the center of the earth to center of reads that's R now dudes this is very simple what we're trying to do is we're trying to figure out the acceleration of gravity way high above the surface of the Earth what happens to the acceleration of gravity is you leave the Earth it gets smaller exponentially right cuz R is squared so for example what if you double your distance from the center of the earth if you double r what's going to happen to gravity time 1/4 what if you Triple R Time 1 nth it'll be right it's exponential okay so how do we figure out this equation because you have to know this equation rather than just memorize it I would like you to understand where it comes from and it's very simple look so read is a track to the Earth right and that is a gravitational force of attraction and by the way guys is the earth attracted to re yes right no Force exists in isolation if Reed is attracted to the Earth that means the Earth is attracted to Reed now guys what was the first equation what was the first equation that you ever learned for force of gravity going way back to like September m g where this would be what mass of Earth or mass of Reed mass of Reed because we're focusing on Reed here right we're focusing on this point up here okay so the gravitational the gravitational force on Reed is equal to mass of Reed times the acceleration of gravity but what I just showed you today is there is a second equation for the gravitational force between objects what's the the second equation Big G M1 M2 over R 2 there are two equations for the force of gravity so you set these equal to each other sorry Reed what happens to your mass it cancels so it doesn't matter it doesn't matter if this was Reed or a bag of potato chips or a tennis ball it doesn't matter what it is cuz it cancels out M2 cancels out and notice what you're left with you're left with this equation so guys let me ask you a question here what if you had some unknown Planet let's let's say you're on the AP exam let's say that you're on the AP exam and they give you a planet okay and they want you to find gravity on the surface of the planet what two things would you need to know to find the acceleration of gravity on the surface of the planet yo the mass of the planet the mass of the planet the radius and the radius of the planet if you know those two things you can find gravity on the surface of that planet okay second application and then we're done okay the second application for Newton's law of gravitation has to do with one object orbiting another object like the moon around the Earth or the Earth around around the Sun and I just want to mention by the way both of both of those things that I just mentioned are actually elliptical paths you guys know what an ellipses it's a circle that has been smooshed and there's different degrees to an ellipse they call that what the the exent eccentricity so guys for this class you want to know what we're going to do for elliptical motion we're just going to say h it's close enough to a circle okay and that's he that's college board approved we are going to say that this orbit here this orbit we're going to call it we're going to call it circular so say say that this is the moon so we'll call this M2 and then the Earth is M1 now guys we're going to look at forces right now so what does this V represent this V is the tangential velocity of the Moon around the earth okay now what distance will be important in fact hold up I want I'm going to erase this velocity because we're going to we're going to look at forces I'm going to erase the velocity because we're not concerned with that right now uh the distance that we're going to need is from the center of the earth to the center of the Moon R right now is the earth an object yes is the moon an object yes so these forces are gravitational forces right it's a gravitational force of attraction now look at this look right here what is the only force acting on M2 which I'm saying is the moon so focusing on M2 if we sum the forces what's the only force acting on the moon it's the gravitational force notice that the gravitational force points to the center of this Circle H for an object that's in a circular path what type of acceleration is that centripetal which is caused by a centripetal force so when you sum these forces the only force acting on M2 if you focus in on M2 the only force is the gravitational force sum of the forces equals m a where this would be M2 this is a centripetal because it's in a circular path now we're ultimately going to end up with this right here we're going to end up with this now what is the equation for gravitational force big G M1 M2 over R 2 okay equals M2 now what's the equation for centripetal acceleration centripetal acceleration is V2 over R now this cleans up rather nicely the M2 cancels one of the RS cancels and what you get is v^2 equal G mass of the Earth R which is the same thing as this equation and what's this V so going back to the beginning what's the V so if you look at this satellite right here this Moon it has what we call a tangential velocity and this is how you would find it does the satellites does this moon or whatever it is could be a satellite could be a moon Mo does it does its velocity around the earth depend upon its mass what's this m in this equation is it the mass of the satellite or the mass of the center guy it's the mass of the center guy notice that the mass of the satellite canel out