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let's say we were to take a little excursion to the moon and so here we are sitting on the surface of the moon that's the surface of the Moon right there and with us to our excursion to the moon we brought two things we brought ourself a concrete brick so that's my brick right over there that's my concrete brick all that's orange all it will say it's an orange concrete brick and I also brought a bird feather with us so this is the bird feather so this is the bird feather and then my question to you is if I were to hold both of the brick and the bird feather at the same time and I were to let go of both of them at the same time and ask you which one of them would hit the surface of the Moon first what would you say well if you base it on your experience on earth on earth if you were to take a brick and a feather a brick would fall which just goes straight down a brick would just immediately fall to the earth and it would do it quite quickly it would accelerate quite quickly while a feather would kind of float around if you had a feather on on earth on earth it would just kind of you know float around it would go that way then would go that way and it would make it would slowly make its way down to the ground so on earth at least in the presence of air it looks like the brick will hit the ground first but what would happen at the moon and what's interesting about the moon is we have no atmosphere we have no air to kind of provide resistance for either the brick or the feather so what do you think is going to happen so your first temptation would say well let's just use the let's just use the law the universal law of gravity so what is the force of gravity on the brick so the force on the brick well you could calculate that out the force of gravity on the brick is going to be equal to big G is going to be equal to big G times the mass of the moon I'll say the that's an M for mass and then the subscript is lowercase M for moon the mass of the moon times the mass of the brick times the mass of the brick divided by divided by the distance between the brick and the center of the Moon squared so this is the distance between the brick and the center of the Moon and you square it fair enough that's the force on the brick what's going to be the force on the feather the force due to gravity on the feather or another way to think about it the weight of the feather on the moon so what is the force on the feather we'll do the same calculation the force on the feather the force on the feather is going to be equal to big G big G times the mass of the moon times the mass of the feather times the mass of the feather divided by the distance between the center of this feather and the center of the Moon squared that's the distance and then we squared so if you look at both of these if you look at both of these expressions they both have this quantity right over here G times the mass of the moon divided by the distance between this height and the center of the Moon squared so they both have this exact expression on it so let's replace that expression let's just call that the gravitational field on the moon so if you apply this number by any mass it'll tell you the weight of that object on the moon or the gravitational force acting downward on that object on the moon so this is the gravitational field of the moon so I'll just call it G sub M and all it is is all of these quantities combined so if we simplify it that way the force on the brick due to the moon is going to be equal to that lowercase G on the moon normally we use this lowercase G for the gravitational constant on earth or the for the gravitational field on earth or sometimes the acceleration of gravity on earth but now we're referring to the moon that's why this lowercase subscript M is doing for us so it's equal to that times the mass of the brick for the case of the feather the force on the feather is equal to all of this business so that's the G sub M is equal to G sub M times the mass of the feather times the mass of the feather so now assuming that the mass of the brick is much greater than the mass of the feather so let's we're going to assume which is a reasonable thing to assume that the mass of the brick is greater than the mass of the feather then the mass of the feather what's going to be their relative forces well here you have a greater mass times the same quantity here you have a less a smaller mass times the same quantity so if the mass of the brick is greater than the mass of the feather it's completely reasonable to say that the force of gravity on the brick is going to be greater than the force of gravity on the feather so if you do all of this and everything we've done to this point is correct you might say hey there's going to be more force due to gravity on the brick and that's why the brick will be accelerated down more quickly but what you need to remember is if there is more force that's being gravitational force on this brick but it also has greater mass and we remember the larger something's mass is the more the larger its mass the less acceleration little experience for a given force so what really determines how quickly either of these things will fall is their accelerations and let's figure out their accelerations so we know that we know that I'll just in a neutral color we know that force is equal to mass times acceleration so if we want to figure out the acceleration of the brick or we could write it the other way the acceleration if we divide both sides by mass we get acceleration is equal to force divided by mass acceleration is equal to force divided by force divided by mass and acceleration is a vector quantity and force is also a vector quantity and in this situation we will we will use we will use well I'll use a well we're not using any actual value so but if I were using actual values I would use negative numbers for downwards and positive values for upwards but we're not using any signs here so but you could assume that the the direction is implicitly being given so what's the acceleration of the brick the acceleration of of the brick it's a lowercase P I was writing the acceleration of the brick is going to be equal to the force applied to the brick the force applied to the brick which is the force applied to the brick divided by the mass of the brick but the force applied to the brick we already know is this business right over here it is little G on the moon the gravitational field on the moon times the mass of the brick and we're dividing that by the mass of the brick so the acceleration on the brick on the moon or the acceleration that the brick will experience is is the same thing as that gravitational field expression it is G sub M is that this is how quickly it would accelerate on the moon now let's do the same thing for the feather and think you see where this is going the acceleration of the feather the acceleration of the feather is going to be the force on the feather the force on the feather divided by the mass of the feather the force on the feather is G sub M G with the subscript M times the mass of the feather times the mass of the feather and then we're going to divide that by the mass of the feather and so once again its acceleration is going to be the same quantity so they are both going to accelerate at the same rate downwards which tells us that they'll both hit the ground at the same rate they'll both accelerate from the same point at the same time and they'll both have the same velocity when they hit the ground and they'll both hit it at the exact same time despite one having a larger mass so the reality is is the larger mass does create a larger gravitational or because it has a larger mass it has a larger gravitational attraction to the moon but because of its mass that attraction gives it the same acceleration as something with a smaller mass so any mass at the same level on the surface of the moon would experience the same acceleration so now you're the quite natural question is wait Sal if that's true on the moon it should also be true on earth and it would be true on earth if you did this exact same experiment and you evacuated all the air from the room so that you didn't have air resistance and you took a brick and a feather and let them go at the same time they will both hit the ground at the exact same time which is little on too unintuitive to imagine a feather just plummeting the same way a brick would but it would if you evacuated all the air and so the answer with what the reason why we see this over here and I think you get the sense because I already talked about evacuating the air is that the difference between the brick and the feather is all due to air resistance if you took the same brick or if you took something that had the same mass as the brick and you were to flatten it out it has more air resistance so if you were to flatten it out if you were to flatten it out but let's say it has the same mass let's say this thing and this thing have the same mass this thing would fall slower than that because it'll have more air resistance it has more air to kind of collide into to provide resistance as it falls and if you took a feather and if you compacted it really really really really really small the same mass as a feather but you made it so small that could kind of cut through the air you'll see that it will drop a lot drop a lot faster so the real difference between how things fall on earth if you had no air they would all fall at the exact same rate it's only because of air that they fall at different rates and the air does two things for constant pressure so if you have two objects that have the same shape the object that is heavier that has more weight will fall faster because it'll overcome it'll be able to it'll provide more net force against the air pressure if you have something that has the same weight the object that is more aerodynamic will fall faster the one that cuts through the one that has the least air resistance and it's a little experiment that you can try in the comfort of your own room right now take a brick or not a brick take a book take a book take a book like this and you could drop it and then you could take another piece of paper or even a little you know postcard or something and you drop it and you'll see of course a postcard will fall much lower than this book but what you do is put the postcard on top of the book so that the book is essentially breaking all the air resistance for the postcard and what you'll see is if you put it on top of the book and you were to drop it you'll see that they followed the exact same rate

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