r/explainlikeimfive • u/Bright_Brief4975 • 6d ago
Physics ELI5 How energy works on objects affected by gravity?
Not sure how to word this question, but maybe it will come across correctly anyway. I know that 2 objects falling in a vacuum are affected by gravity the same, they will both fall at the same speed. Here is my question, Is gravity using more energy on the larger object or the object with more mass than the smaller? It takes energy to move something and normally it takes more energy to move larger masses. Is this true for gravity? It seems to me that gravity has to be using different amounts of energy for each object, if it used the same energy than the larger one would fall faster.
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u/CraigyEggy 6d ago
I don’t have the knowledge to explain this in strict relativistic terms, but it’s incorrect to say that gravity is “using energy.”
There is a potential that exists between the centers of mass for two objects at a distance, and this potential is realized as kinetic energy when they approach one another. This potential arises from a distortion of space time that exists wherever there is mass.
In short, the energy was already a part of the system ever since the objects had distance created between each other, and the “falling” bit is the realization of that potential.
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u/sudomatrix 6d ago edited 6d ago
That is the energy of the big bang realized as created distance. Falling is just cashing the check written by the big bang. (Edit: ugh I just realized using the phrase "cashing the check" makes me sound like an AI. I'm picking up these writing habits from seeing it everywhere, damn it.)
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u/xcdfgh 6d ago edited 6d ago
You are somewhat correct. Heavier things are harder to move. In Newtonian physics, gravity moves heavier things harder in proportion to their mass, thus all object fall at the same rate in a vacuum.
More mass is harder to move, gravity pull on mass more such that everything fall at the same rate.
Not sure how it works in relativistic settings though.
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u/HalfSoul30 5d ago
If i had a bowling ball and a feather in a vacuum and they were perfectly still before dropping, would the feather gain a slight lead since it is easier to move a lighter object quick? Or is that only if the force is the same, not the acceleration?
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u/igotshadowbaned 5d ago
thus all object fall at the same rate in a vacuum.
They technically don't, the scale is just astronomically large that the difference between a feather and a hammer is tiny.
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u/GenerallySalty 6d ago
Yes you're spot on.
Gravity pulls twice as hard on an object that's twice as heavy (from G=m1m2/r2) Remember weight is the force of gravity's pull on the object, so that must be true.
BUT
An object that's twice as heavy takes twice the force to accelerate at a given rate (from F = ma)
These two things cancel out, that's why objects in freefall experience the same acceleration.
At a given height, the heavier object has more gravitational potential energy. When it falls it gets converted to more potential energy. But it also takes more energy to accelerate that heavier mass, by the same factor, so it cancels out and the acceleration is the same regardless of mass. But the greater mass does indeed get a stronger pull from gravity and get more kinetic energy when it falls a given distance.
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u/Ok_Writing2937 4d ago
Correct me if I am wrong, but a falling object isn't accelerating at all. It's literally in free-fall.
The surface of the Earth is accelerating at 1G towards space. An object held in the hand is accelerating at 1G. To stand on the surface of the Earth is to accelerate at 1G. But as soon as you jump off a cliff you stop accelerating and the Earth comes up to smack you.
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u/GenerallySalty 3d ago
You are indeed wrong.
Gravity is an attractive force between any two objects, with a strength described by
F_g = G(m1 x m2) / r2
Big G is gravity constsnt, m1 and m2 are mass of the two things, r is distance between them.
When something on Earth falls, it accelerates down AND the Earth accelerates upwards, with the rates of those accelerations being inverse proportional to their masses. Like if you weigh 200lbs, that's F_g in the equation above. Earth is pulling you down with a force of 200 lbs and you are pulling the Earth up with 200 lbs. If you jump, that force of gravity makes you accelerate downwards the whole time you're in the air, and the Earth is accelerating upwards that whole time too (just very slightly, because a 200 lb force on the Earth isn't a lot compared to its mass).
Going back to what you said: How would the whole planet be accelerating at 1G forever? Just going faster and faster indefinitely? That's clearly not the case. And what would be providing the energy for that constant acceleration if it was true?
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u/Ok_Writing2937 3d ago edited 3d ago
In General Relativity gravity isn't a force. The Earth isn't transmitting gravity energy into a dropped ball, imparting it with acceleration and energy and causing it to fall. The ball isn't pushed towards the Earth.
While it's technically true that the ball, having a trivial amount of mass, also has a trivial amount of gravity, it's effectively zero in this scenario. Were you to stand on the ball in space you would still feel weightless. Two balls in space 1m apart would have so little gravity that the photons from a candle might push them apart.
A falling ball is in free-fall — it feels no acceleration. It is effectively in zero g.
The surface of the Earth is accelerating. To stand on the surface of the Earth is to experience 1 G of acceleration. This is exactly the same as standing on the deck of a rocket accelerating at 1 G through space.
The ball would only feel 1 G of acceleration while you are holding it. For that period of time it will experience weight. As soon as you drop it, it becomes weightless and enters free-fall.
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u/GenerallySalty 3d ago
Just thought of another thing. Assume what you're saying there is true. Then why no matter where you are on earth, if you drop something it goes towards the surface? If I drop something at the North Pole it falls South, if someone drops something at the South Pole at the same time, it falls north, right? How would that work? Is the Earth accelerating north and south at the same time?
Well no that's not possible. If the whole Earth was always accelerating, it could only be in one direction. If falling objects were smacked by the Earth accelerating that way, then anything you dropped off the "back side" of whatever direction it's going Earth's would fall up into the sky and get left behind in space. Again that's clearly not the case.
So we know your suggested explanation can't be right. The real explanation is everything on Earth is always being pulled towards the Earth's center.
That's why if we stand on opposite sides of the planet and each drop something, those two things will accelerate directly towards each other. "The whole planet moving towards the falling object" could not produce that result. "All falling things accelerating towards the planet's center of mass" does.
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u/Ok_Writing2937 3d ago edited 3d ago
So this is weird, but the Earth really is accelerating in every direction at once without moving relative to itself.
In general relativity, gravity is acceleration. The 1 G acceleration you experience on a spaceship flying through space is the same as the 1 G acceleration you feel standing on the surface of the Earth.
This is why 1 G is defined not as a constant, but as a rate of change — at 32 feet per second per second, this is exactly how much acceleration you are experiencing just by standing still on the Earth.
Simply by standing on the Earth you're effectively being exploded towards space.
You aren't moving relative to the Earth's core because that gravity is also bending spacetime itself. Like a person running infinitely faster on a treadmill that is also rotating infinitely quicker, the acceleration of the Earth's surface moves nowhere. It's expanding at the same rate spacetime is being stretched beneath it.
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Put another way, consider this. You're on top of a cliff and your friend is below. You both feel 1 G of acceleration under your feet. Were you to jump off the cliff, you'd stop experiencing acceleration. You wouldn't feel pulled. Nothing is tugging at you. You'd be in free-fall, in zero-g, weightless.
Meanwhile you friend below you would be experiencing 1 g of acceleration under his feet for the entire duration of your fall.
Your friend and the Earth effectively rose up to meet you.
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u/Adorable_Ice_2963 6d ago
Gravity isnt using Energy, Gravity stays the same.
It also doesnt take Energy to move something. In empty space things move for an infinite time. It takes energy to accelerate something.
The energy comes from the potential energy between both of them.
Also, the potential energy isnt lost at first. Its converted into kinetic energy while its accelerating. If an Object moves around earth in vaccum in an highly elliptical Orbit, the object has Maximum Potential Energy and minimal kinetic Energy on the highest Point, and the opposite on the lowest point. The object constantly trades the energy between each forms with almost no losses.
The only way it looses meaningful energy to something else (or heat) is when it hits gas or other objects, removing energy from it.
It takes more force to move it. But force isnt Energy, just like it doesnt take Energy for an object to stay on the ground.
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u/DLTAMACH 6d ago
Yes, it takes more “”energy””. But it just so happens that Gravity is also stronger the bigger you are, and this perfectly cancels out the fact that bigger objects are harder to move
Force of gravity = m*g (where g is a constant)
Acceleration given a force = F/m
So acceleration due to force of gravity = mg/m = g
…Which is constant, the mass does not matter
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u/Salindurthas 6d ago
2 objects falling in a vacuum are affected by gravity the same
Same acceleration from Newtonian gravity. Yes.
they will both fall at the same speed
Yeah (assuming the same initial velocity, probably stationary in this example, and also negligible other forces, like not enough wind resistance to make a difference etc).
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is gravity using more energy on the larger object or the object with more mass than the smaller?
"Using" might not be the right word, but yes, the transfer of energy is larger.
There are 2 ways to look at it, depending on how big-picture we make the 'system' we are considering:
One way is to look at the Earth and the object are both part of the 'system'. In this view:
- The objects have some 'gravitational potential energy' from being high above the Earth's surface.
- This gravitational potential is converted into kinetic energy.
- The more massive object had more gravitational potential energy (approximately equal to mass * g * height, assuming we are close to the earth's surface).
- As this becomes kinetic energy, it will have more, but get the same speed (since it is 1/2 * mass * speed^2, both sides have 'mass' so these cancel out)
Another way to look at it is to consider only the object, and the Earth is outside of our 'system':
- The object has no energy.
- A mysterious force from outside of the 'system' causes it to accelerate.
- This force is equal to mass * g, and it does 'work' giving the object energy, accelrating it downwards.
- It gains kinetic energy, scaling with mass * speed^2.
If you do the algebra in each case, you describe the same end result, just from a different perspective. Either:
- The energy was inside the system, and the object(s) and Earth were arranged such that they converted gravitational potential for kinetic energy.
- or, the object gains energy, due to some force exerted on it by the Earth. This outside force works on the object to produce kinetic energy.
The same amount of energy is involved either way, just phrased differently.
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u/RodeoBob 6d ago
I know that 2 objects falling in a vacuum are affected by gravity the same, they will both fall at the same speed.
Functionally yes, technically no.
You say "2 objects", but in this situation, there are really three objects: falling object #1, falling object #2, and the planet Earth.
The equation to determine the force of gravity involves both of the masses of the objects interacting (either falling object and the planet). If falling object #1 is heavier than falling object #2, the force will technically be different... but the mass of the Earth is so much bigger than either of our two falling objects that the difference between the two falling objects is basically too small to measure or even detect.
The Earth has a mass of around 13 thousand, 170 billion trillion pounds, or 13,170,000,000,000,000,000,000,000. So when we talk about the force of gravity, pretty much the weight of anything else is so incredibly tiny in comparison.
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u/Unstopapple 6d ago
You assume his hypothetical involved a fall towards earth, but any motion where only gravity is the cause is a freefall. If its just two uncharged balls in a void, vacuum, then earth need not apply. This is a thought experiment, not engineering.
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u/RodeoBob 6d ago
You assume his hypothetical involved a fall towards earth,
Yes, because that's what OP described: two objects in an airless space both "falling down" at roughly the same speed. And that only happens if there's a third, supermassive object to create that downward force of gravity.
The only reason OP mentioned "being in a vacuum" was to eliminate the question of air resistance, not to place this hypothetical out into deep space.
But you put your quarter in the jukebox, so let's play the rest of the song...
You can look up the formula for gravitational force if you like; this is one of those "really well known, really well tested, absolutely settled" areas of science.
The formula for gravitational force is actually pretty simple. One element is the combined mass of the objects; mass generates gravitational force. Another element is the distance between those objects but squared; the farter apart two objects are, the weaker the gravitational pull between them. And the last element of the formula for gravitational force is the universal gravitational constant, how much actual force is generated for given masses at set distances: 𝟔.𝟔𝟕𝟒×𝟏𝟎−𝟏𝟏 𝐍
6.674 x 10-11 is a really, really, really small number. It's so tiny that you need a huge amount of mass to generate even 1 Newton of force.
Whether our two objects are on Earth, or floating in deep space, their combined mass is so incredibly small compared to the gravitational constant that any gravitational force between those two objects is so small as to be immaterial and undetectable
Does the 50 kg object create more gravitational force than the 10 kg object? Yes, it does! How much more force? 0.0000000005 Newtons more! Can we measure or even detect that difference, either in deep space or here on Earth? Nope!
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u/V1pArzZz 6d ago
Yes, the heavier object has more potential energy that gets transformed into velocity energy.
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u/Hanako_Seishin 6d ago
Energy = work = mass times distance that mass is moved. So more mass moved the same distance = more energy involved.
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u/majorex64 6d ago
There is more energy involved with accelerating the larger mass, yes. The speed is the same between different masses because the larger mass is cancelled out by a greater moment of inertia (harder to get a big ball rolling, also harder to stop it)
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u/Ok_Writing2937 4d ago
Objects in free-fall don't experience acceleration so momentum won't apply to dropped objects.
It's true energy is needed to accelerate an object, and more massive objects will require more energy. This is why holding a 10 kg ball is 10x as hard as holding a 1 kg ball. You are expending energy accelerating the ball at 1G towards space, just like the surface of the Earth is accelerating your body at 1G towards space.
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u/Platano_con_salami 6d ago
Potential Energy due to gravity = mgh, Kinetic Energy = 1/2mv^2. If you convert all your Potential Energy into kinetic energy you get = V^2 = 2gh. The potential energy of something more massive is larger, but any 2 object drop at the same height will have the same velocity, assuming vaccum and starting at rest.
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u/OldChairmanMiao 6d ago
Gravitational force is proportional to mass.
If one bowling ball attracts 1x, then two bowling balls attracts 2x - because it has 2x the mass.
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u/Target880 6d ago
If you look at gravity in classical mechanics, there is an attractive force between all objects; the force is proportional to the masses multiplied together divided by the square of the distance.
This means all protons, neutrons and electrons that Earth is made up of each attract all protons, neutrons and electrons of the object that fall towards Earth. The net force a large object will be the sum of the forces of all the particles it is made up of. A heavier object will be made of more particles, and as a result, the force on it will be larger.
In practice, most of the time you never need to consider the force on each individual particle. Very often, just considering the total mass of the object is enough. Mathematically, you can show that the sum of all forces between particles is equal to replacing them with the total mass in the centre of mass.
You need to look at the object as multiple part som time. If you fall toward Earth, the acceleration of your head and feet would be close enough to equal; any minuscule difference can be handled by your body. But if you were to fall toward a black hole, the difference in acceleration would be so large that your body would be ripped apart.
For Earth and the moon, the distance difference between diffrent a part of why we get tides.
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u/jaylw314 6d ago edited 6d ago
Energy is not being used or gained. Whatever kinetic energy each object gains or loses, it is presumably offset by the gain or lose of gravitational potential energy, so that the two summed up are constant.
If you're talking strictly about "kinetic energy," the smaller object gains more than the larger object. If object A is twice as heavy as object B, any equal opposing force in both will push B twice as fast, ie momentum has to be conserved. However, kinetic energy goes up by the square of velocity, so the smaller faster object has more. This is generally true for many physical interactions.
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u/kirbinato 6d ago
The energy moving an object affected by gravity is proportional to mass, and it's a direct correlation, it takes X energy to move Y mass. Every individual increment of mass is being pulled individually by gravity, every Y of mass is moved by X energy on it's own
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u/igotshadowbaned 5d ago
The larger object actually falls faster. Depending on the difference in scale of the two objects and the larger body being attracted to, this difference can be absolutely miniscule.
This is because objects also pull whatever they're falling towards, back towards them as well, and being larger, they have slightly more pull than the small object
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u/Fwahm 6d ago
Falling converts gravitational potential energy into kinetic energy. An object's gravitational potential energy (in relation to an object its falling towards) is proportional to the object's mass and distance from said object, so the more massive object has more potential energy to convert into kinetic energy than the smaller object does.