Want to piss off your friend even more? here is some cool information about why the sun isn't where it looks where it is: ruclips.net/video/9hmeUypGe8M/видео.html
Thats what i thought aswell, and i tried to speak to other people about that, but they dont seem to get what i mean. Thanks for making this video, so i can show them...
But why do i feel the time is being increased because 2 big objects (Large Mass objects) are just bending space time around each other increasing the overall interactions "bend" therefore increasing the rate of speed
Cool. This has always bothered me, that we're taught how 'wrong' aristotle was pretty much alongside the law of universal gravitation, which shows that M2 effects the force/acceleration. Of course it's such a miniscule amount it should be discounted, but it's still true in theory. Or is it? When you see someone answering the question 'do heavy objects fall faster' on something like yahoo answers, they're always just (rightly enough) ignoring the M2 because it makes negligible difference, but one time i recall reading a more in-depth discussion of the forces involved, where... i forget, but something about if you drop them at the same time, b/c the heavier object is pulling the earth more (again, an infinitesimally small amount, but still more), the time would not be different? I remember not being sure of the explanation, but it seems like there's the different levels of 1) our ignorant intuition that heavy things should fall faster, then 2)our understanding that (basically) everything falls at 9.8m/s^2, then 3)as per this video, that M2 is still at play, then 4) some further consideration?
Well first of all, on earth these fores for m2, the earth, is so weak, i'm sure some other force or assumption will break the idea - So it only makes sense to talk about theoretical and in a idealized world. We are only working with Rigid bodies and are neglecting a lot of things. But yea, you are right. I did some simulations, showing that if 3 Objects are dropped at the same distance (like hammer, feather and moon) they will all collide at the same time, NO matter what mass they have. However, when the distance was not the same, the lighter object would actually arrive first, because it got accelerated way more than the heavier objects. But take a look at the physics exchange link i provided, there's more info on that there.
I can explain. A larger force is required to accelerate a larger mass by the same amount. The formula F = ma can be rearranged for the acceleration of gravity a = F/m . A larger mass requires a larger force, however the acceleration of gravity is the same for both objects. The only reason heavier objects fall faster than lighter objects on Earth is because of air resistance. Heavier objects take longer to reach terminal velocity. Depending on the height at which both objects are released, the lighter object may have enough time to reach terminal velocity while the heavier object would continue to accelerate, achieving a higher top speed before reaching its own terminal velocity.
@@Monochromicornicopia light and heavy object would both fall at the same rate in a vacuum towards earth, however the earth will fall towards the object at a different speed depending on the objects mass
Note that this is only the case when the two objects are dropped separately. If the objects are dropped together, the single Earth will accelerate towards both objects and hit them at the same time.
The Earth doesn't accelerate much toward the falling object (less than the radius of a proton), so its pretty useless to think of the Earth as "moving upward" to meet the object.
This is a theoretical exercise using Newtonian mechanics. It doesn't matter by how much the Earth moves. The question is about whether a heavier object and the Earth will meet more quickly or not. It doesn't matter how minuscule the difference is. (note: I made another comment which raises an issue against the claim that the heavier object will collide with the Earth more quickly).
not exactly correct. the objects need to be side by side for this to work. directly side by side. just put distance between them and what you say is no longer correct because each of these objects exert pull on the earth in DIFFERENT directions. as an extreme case, what if the objects are so far away as to be on exact opposite ends of the planet?
Newton and galileo They bouth right Everything Thats is far lighter then planet earth will fall in vacum at the same time if the length of the fall is not to far But if ther is a way to test some object that is similar in weight to planet earth or slightly heavier The result would be diferent. Such an object would surely fall twice as fast, better express is, such an object would meet faster earth instead to fall on earth. Because both objects would move towards each other. It is the electromagnetic force that is the main force in the universe
So basically heavier objects fall faster. But the heavy objects in our world are not heavy enough compared to earth in order to produce a statistically significant change in the value of acceleration due to gravity, g.
The _only_ object within the Earth's sphere of influence with enough mass to make the effect described in this video detectable is the Moon. Everything else within a distance of about 1.5 million km is too small compared to Earth.
A 10 kg object is the same as ten 1 kg objects stuck together. How could the 10 objects stuck together fall faster than any of its 1 kg component objects alone simply because they were stuck together? It's the same if you consider the gravity produced by the object/objects, each 1 kg of the 10 kg object produces the same gravity as a single independent 1 kg object.
That’s only true if the gravitational force is more than the object. The sun Would fall faster than the earth because its gravitational pull is higher due to its mass. ^ the same is true for all heavier objects with the same shape. In our world, the difference is barely quantifiable. It’s barely quantifiable because 8 or 10 pounds is laughably inconsequential to the weight of the earth. But it is quantifiable.
@@Ash-ng4mn It's actually weird that more massive objects have faster gravitational acceleration of other objects, considering it's just a bunch of less massive objects stuck together.
@@aliengrey1708 The bunch of less massive objects stuck together will pull more strongly on Earth than a single, less massive object will do. However, if a massive and less massive object are dropped _side by side,_ they will hit Earth at the same time since the massive object will pull the Earth towards the less massive object as well as towards itself.
Thought 2 ..the force of gravity varies with distance to the center of gravity...ie the force 9.8m/sec^2, at the earths surface, is a higher value closer to the center of earth and less as you go away from the surface. It varies by an integral I believe..and have always liked to derive the equation of gravity acceleration variance by distance, since learning about it many years ago...
I thought of an issue that might cancel out this difference. Imagine two hammers: 1 kg and 2 kg. Place the 1 kg hammer on the ground and drop the 2 kg hammer and let it and the Earth collide. Now leave it on the ground and pick up the 1 kg hammer. The Earth now has a mass of 1 kg more since the 2 kg hammer has replaced the 1 kg hammer as part of the Earth. The gravitational force of the new more massive Earth will be larger than before creating a larger acceleration on the 1 kg hammer. Perhaps this will cancel the slower acceleration of the Earth towards the 1 kg hammer?
yes you are correct. anyway while you're correct, what your saying is sort of besides the point.... the point was simply that if you have two mutually attracted objects (a and b) in space, then the time that it takes for them to collide is a function not only of the acceleration of a in the direction of b due to gravity but also of the acceleration of b in the direction of a due to gravity.
It will cancel out exactly, assuming point masses and uniform spherical gravitational fields, of course. The gravitational acceleration of two bodies toward each other, the time it takes to collide, is proportional to the sum of their masses, regardless of how that mass is distributed between them. Two bodies with half the mass of the Earth would also accelerate toward each other at ~9.82... m/s^2 at a distance of ~1 Earth radius.
I wondered the same as well regarding fall times and came to the same conclusion...also 10^-24 is so small(as you have aptly demonstrated) I wonder if other effects on the "surface of earth" of temperature or magnetism or ...etc may actually contribute more to the acceleration....There is a latest video on Numberphile regarding darts thrown at a dartboard..it is interesting that mathematics can come up with probabilities and solutions that, in the physical world are indeed "possible". (In the Numberphile case I mention of the dartboard for the initial conditions the bullseye and boarder were probability zero, which we all know are possible even for beginners in darts). This struck me because current quantum mechanics is all about the probability wave equation. This equation is a model and not necessarily what happens "in the real world". And in fact we do see the macroscopic effects..keep up the great videos..I subscribed.
The Earth doesn't accelerate much toward the falling object (Earth moves by less than the radius of a proton), so its pretty useless to think of the Earth as "moving upward" to meet the object.
well that depends on the mass of the "falling" object right? in this case it was an imaginary object with the mass of earth (and the density of a neutron star).
Want to piss off your friend even more? here is some cool information about why the sun isn't where it looks where it is: ruclips.net/video/9hmeUypGe8M/видео.html
Thats what i thought aswell, and i tried to speak to other people about that, but they dont seem to get what i mean. Thanks for making this video, so i can show them...
But why do i feel the time is being increased because 2 big objects (Large Mass objects) are just bending space time around each other increasing the overall interactions "bend" therefore increasing the rate of speed
Should we not use general relativity to calculate dropping a neutron star? Its a more accurate discription of gravity and time.
Definitely - i just used a neutron star to prove my point
Cool. This has always bothered me, that we're taught how 'wrong' aristotle was pretty much alongside the law of universal gravitation, which shows that M2 effects the force/acceleration. Of course it's such a miniscule amount it should be discounted, but it's still true in theory.
Or is it? When you see someone answering the question 'do heavy objects fall faster' on something like yahoo answers, they're always just (rightly enough) ignoring the M2 because it makes negligible difference, but one time i recall reading a more in-depth discussion of the forces involved, where... i forget, but something about if you drop them at the same time, b/c the heavier object is pulling the earth more (again, an infinitesimally small amount, but still more), the time would not be different? I remember not being sure of the explanation, but it seems like there's the different levels of 1) our ignorant intuition that heavy things should fall faster, then 2)our understanding that (basically) everything falls at 9.8m/s^2, then 3)as per this video, that M2 is still at play, then 4) some further consideration?
Well first of all, on earth these fores for m2, the earth, is so weak, i'm sure some other force or assumption will break the idea - So it only makes sense to talk about theoretical and in a idealized world. We are only working with Rigid bodies and are neglecting a lot of things.
But yea, you are right. I did some simulations, showing that if 3 Objects are dropped at the same distance (like hammer, feather and moon) they will all collide at the same time, NO matter what mass they have. However, when the distance was not the same, the lighter object would actually arrive first, because it got accelerated way more than the heavier objects. But take a look at the physics exchange link i provided, there's more info on that there.
I can explain. A larger force is required to accelerate a larger mass by the same amount. The formula F = ma can be rearranged for the acceleration of gravity a = F/m . A larger mass requires a larger force, however the acceleration of gravity is the same for both objects.
The only reason heavier objects fall faster than lighter objects on Earth is because of air resistance. Heavier objects take longer to reach terminal velocity. Depending on the height at which both objects are released, the lighter object may have enough time to reach terminal velocity while the heavier object would continue to accelerate, achieving a higher top speed before reaching its own terminal velocity.
@@Monochromicornicopia light and heavy object would both fall at the same rate in a vacuum towards earth, however the earth will fall towards the object at a different speed depending on the objects mass
@@baumeisterjack9281 Which is why I clarified both vacuum and non vacuum solution.
Omg you're the best , best explanation ever
ty man!
Very well said , excellent demonstration truly Genius work !
Note that this is only the case when the two objects are dropped separately. If the objects are dropped together, the single Earth will accelerate towards both objects and hit them at the same time.
The Earth doesn't accelerate much toward the falling object (less than the radius of a proton), so its pretty useless to think of the Earth as "moving upward" to meet the object.
This is a theoretical exercise using Newtonian mechanics. It doesn't matter by how much the Earth moves. The question is about whether a heavier object and the Earth will meet more quickly or not. It doesn't matter how minuscule the difference is. (note: I made another comment which raises an issue against the claim that the heavier object will collide with the Earth more quickly).
not exactly correct. the objects need to be side by side for this to work. directly side by side. just put distance between them and what you say is no longer correct because each of these objects exert pull on the earth in DIFFERENT directions. as an extreme case, what if the objects are so far away as to be on exact opposite ends of the planet?
I just though about this and looked it up.
3:23 I'm guessing that r_i is the initial radius but what is r_f?
It's inital distance and final distance
Newton and galileo
They bouth right
Everything Thats is far lighter then planet earth will fall in vacum at the same time if the length of the fall is not to far
But if ther is a way to test some object that is similar in weight to planet earth or slightly heavier The result would be diferent.
Such an object would surely fall twice as fast, better express is, such an object would meet faster earth instead to fall on earth.
Because both objects would move towards each other.
It is the electromagnetic force that is the main force in the universe
So basically heavier objects fall faster. But the heavy objects in our world are not heavy enough compared to earth in order to produce a statistically significant change in the value of acceleration due to gravity, g.
The _only_ object within the Earth's sphere of influence with enough mass to make the effect described in this video detectable is the Moon. Everything else within a distance of about 1.5 million km is too small compared to Earth.
A 10 kg object is the same as ten 1 kg objects stuck together. How could the 10 objects stuck together fall faster than any of its 1 kg component objects alone simply because they were stuck together? It's the same if you consider the gravity produced by the object/objects, each 1 kg of the 10 kg object produces the same gravity as a single independent 1 kg object.
That’s only true if the gravitational force is more than the object. The sun Would fall faster than the earth because its gravitational pull is higher due to its mass.
^ the same is true for all heavier objects with the same shape. In our world, the difference is barely quantifiable. It’s barely quantifiable because 8 or 10 pounds is laughably inconsequential to the weight of the earth. But it is quantifiable.
@@Ash-ng4mn It's actually weird that more massive objects have faster gravitational acceleration of other objects, considering it's just a bunch of less massive objects stuck together.
@@aliengrey1708
The bunch of less massive objects stuck together will pull more strongly on Earth than a single, less massive object will do. However, if a massive and less massive object are dropped _side by side,_ they will hit Earth at the same time since the massive object will pull the Earth towards the less massive object as well as towards itself.
@@fromnorway643 You could be right, it's probably not exactly the same fall rate, just so close to the same that it would be difficult to detect.
what was that nasa 5$ video , was that legit 😂
Thought 2 ..the force of gravity varies with distance to the center of gravity...ie the force 9.8m/sec^2, at the earths surface, is a higher value closer to the center of earth and less as you go away from the surface. It varies by an integral I believe..and have always liked to derive the equation of gravity acceleration variance by distance, since learning about it many years ago...
Great
I thought of an issue that might cancel out this difference. Imagine two hammers: 1 kg and 2 kg. Place the 1 kg hammer on the ground and drop the 2 kg hammer and let it and the Earth collide. Now leave it on the ground and pick up the 1 kg hammer. The Earth now has a mass of 1 kg more since the 2 kg hammer has replaced the 1 kg hammer as part of the Earth. The gravitational force of the new more massive Earth will be larger than before creating a larger acceleration on the 1 kg hammer. Perhaps this will cancel the slower acceleration of the Earth towards the 1 kg hammer?
yes you are correct. anyway while you're correct, what your saying is sort of besides the point.... the point was simply that if you have two mutually attracted objects (a and b) in space, then the time that it takes for them to collide is a function not only of the acceleration of a in the direction of b due to gravity but also of the acceleration of b in the direction of a due to gravity.
It will cancel out exactly, assuming point masses and uniform spherical gravitational fields, of course. The gravitational acceleration of two bodies toward each other, the time it takes to collide, is proportional to the sum of their masses, regardless of how that mass is distributed between them. Two bodies with half the mass of the Earth would also accelerate toward each other at ~9.82... m/s^2 at a distance of ~1 Earth radius.
I wondered the same as well regarding fall times and came to the same conclusion...also 10^-24 is so small(as you have aptly demonstrated) I wonder if other effects on the "surface of earth" of temperature or magnetism or ...etc may actually contribute more to the acceleration....There is a latest video on Numberphile regarding darts thrown at a dartboard..it is interesting that mathematics can come up with probabilities and solutions that, in the physical world are indeed "possible". (In the Numberphile case I mention of the dartboard for the initial conditions the bullseye and boarder were probability zero, which we all know are possible even for beginners in darts). This struck me because current quantum mechanics is all about the probability wave equation. This equation is a model and not necessarily what happens "in the real world". And in fact we do see the macroscopic effects..keep up the great videos..I subscribed.
The Earth doesn't accelerate much toward the falling object (Earth moves by less than the radius of a proton), so its pretty useless to think of the Earth as "moving upward" to meet the object.
well that depends on the mass of the "falling" object right? in this case it was an imaginary object with the mass of earth (and the density of a neutron star).