- #1
zuz
- 82
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Hypothetically, if the universe was completely empty, and two apples were 10,000,000,000 light years apart, would their gravity be strong enough to eventually bring them together?
Google for "Newton Law of Gravity", then try calculating it for yourself.zuz said:Me! No. I can't. That's why I asked PF.
...10,000,000,000 light years...HallsofIvy said:So, in this case, where r is 10,000,000 light years, r squared is going to be very, very, large, the gravitational force very, very, small but still non-zero.
Yeah, but since the op posits a magical universe (apples without apple trees as just one example) we can just decide that the HUP doesn't exist there.FactChecker said:PS. I can't resist throwing out an ignorant, amateur thought here. The forces and escape velocity may be so tiny that the uncertainty principle becomes relevant.
As mentioned by Ibex, the escape velocity for an apple is really, really, really small. This, in turn, means that the collision speed between the two apples, even if they start 10 million light years apart, is going to be of similar magnitude. Not even enough to produce any significant bruising, let alone applesauce.HallsofIvy said:That force will slowly increase so the speeds will slowly increase until, after millions of years the two apples will smash together creating the only apple sauce in the universe!
(And leaving us to ask "where are the apple trees?)
The escape velocity at 10^10 light year is 4.2*10-16m/s (assuming a 0.1 kg apple)FactChecker said:PS. I can't resist throwing out an ignorant, amateur thought here. The forces and escape velocity may be so tiny that the uncertainty principle becomes relevant.
I get a somewhat smaller figure - about 3.8×10-19m/s.willem2 said:The escape velocity at 10^10 light year is 4.2*10-16m/s
Yes, you're right.Ibix said:I get a somewhat smaller figure - about 3.8×10-19m/s.
Does this follow?Janus said:As mentioned by Ibex, the escape velocity for an apple is really, really, really small. This, in turn, means that the collision speed between the two apples, even if they start 10 million light years apart, is going to be of similar magnitude. Not even enough to produce any significant bruising, let alone applesauce.
Apply energy conservation:DaveC426913 said:Does this follow?
Escape velocity is the speed that an object would have to have at some distance "R" from the center of mass, in order to never fall back. So imagine you have your two in-falling apples, and instead of hitting, they started with just enough sideways motion to just skim past each other with their centers 8cm apart. At that point, they would have almost exactly at the same speed as they would have had in the moment just before they touch, if they had fallen directly towards each otherDaveC426913 said:Does this follow?
I guess I'd have to calculate their final velocity after falling 10 million (billion!) light years.
If their velocity is initially zero at near enough infinity to make no difference, their velocity at impact will be the escape velocity from their center-to-center distance at impact.DaveC426913 said:Does this follow?
I just realized that this is trivially true, since it's reversible.DaveC426913 said:TIL.
So, an object, initially at rest WRT Earth, falling from infinity, will be going 11.2 km/s at impact (sans atmo and all other confounding factors)?
<rant>kuruman said:Just out of curiosity, I calculated the time it would take for the two apples to collide if they were released 10 million light years apart.
[mea culpa]DaveC426913 said:<rant>
OHMYGOD.
Billion!
The OP's example was 10 billion light years separation!
(see post 8 if you think I'm overreacting...)
</rant>
The concept refers to a thought experiment in which two apples are placed 10 billion light years apart in an otherwise empty universe, with no other objects or sources of gravity present. It is used to illustrate the strength and universality of the force of gravity.
Despite being placed 10 billion light years apart, the two apples would still be attracted to each other due to the force of gravity. This is because gravity is a fundamental force that acts over large distances and is not affected by the presence or absence of other objects.
Gravity is considered a universal force because it affects all objects in the universe, regardless of their size, mass, or distance from each other. It is responsible for the formation and movement of celestial bodies, as well as the interactions between objects on Earth.
The strength of gravity decreases with distance. This is described by the inverse square law, which states that the force of gravity between two objects is inversely proportional to the square of the distance between them. This means that the farther apart two objects are, the weaker their gravitational attraction will be.
Gravity cannot be shielded or canceled out. Unlike other forces, such as electromagnetism, there is no known way to block or negate the effects of gravity. It is a fundamental force that is always present and cannot be eliminated or avoided.