Gravity: Empty Universe & 2 Apples 10B Light Years Apart

  • I
  • Thread starter zuz
  • Start date
  • Tags
    gravity
In summary: Hey, that's no longer a hypothetical question! In fact, it's one that astronomers have been trying to answer for some time now. The short answer is, we don't know for sure. We can only make educated guesses based on current understanding of physics and our observations of the universe. But even then, there are still many unknowns and uncertainties.In summary, in a completely empty universe, it is difficult to predict how physics would behave since our physical laws may not apply. However, if we make assumptions and use our current understanding of physics, we can estimate that the gravitational force between two apples 10,000,000,000 light years apart would be very small but non-zero. As they start moving towards
  • #1
zuz
82
32
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?
 
Physics news on Phys.org
  • #2
What do you think and why? Can you calculate the force between the two apples if you make reasonable assumptions about their mass?
 
  • #3
Me! No. I can't. That's why I asked PF.
 
  • #4
It's difficult to know how physics would behave in a completely empty universe, since it isn't clear that our physical law would apply to such a universe. That's not what it produced, after all.

However, making the assumption that we could use our physical law, the answer is that it depends on things you haven't stated. The gravitational force between two bodies goes as ##1/r^2##, so never goes to zero as far as we are aware. However, an object which has escape velocity is one going fast enough that the slowing effect of gravity isn't enough to ever stop it. The escape velocity against the gravitational field of an apple is incredibly low. If the apples aren't stationary or moving together, then they'll probably never come together.
 
  • Like
Likes FactChecker
  • #5
zuz said:
Me! No. I can't. That's why I asked PF.
Google for "Newton Law of Gravity", then try calculating it for yourself.
 
  • #6
"Newton's law of gravity", referred to by Nugatory, says that [tex]F= \frac{GMm}{r^2}[/tex] where F is the force between two objects of masses M and m with distance r between them. G is a "universal" constant, its specific value depending on the units used. In the "MKS", "Meter-Kilogram-second", system, it is [itex]6.67\times 10^{-11}[/itex] Newton meters-squared per kg squared.

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. With no other masses in the universe, the "apples" will each apply a very, very, small force on the other so will start moving very, very, slowly toward each other. 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?)
 
  • #7
Cool. Thanks.
 
  • #8
Correction:
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.
...10,000,000,000 light years...
...very, very, very large...
...very, very, very small...

:oldbiggrin:
 
  • #9
Remember that there is an escape velocity that allows one mass to go infinitely far away from another mass. In the case you present, the escape velocity would be extremely small.

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.

EDIT: I didn't notice that @Ibix had already mentioned the escape velocity in an early post (#4).
 
Last edited:
  • #10
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.
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. :smile:
 
  • Haha
Likes FactChecker
  • #11
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?)
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.
 
  • Like
Likes russ_watters and PeroK
  • #12
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.
The escape velocity at 10^10 light year is 4.2*10-16m/s (assuming a 0.1 kg apple)
You're still fine with the uncertainty principle for the radial speed, but what about the tangential speed? If that is even a very tiny fraction of the escape velocity of 4.2*10-16m/s the apples will never come near each other, but go in orbit.
 
  • Like
Likes FactChecker and Ibix
  • #13
willem2 said:
The escape velocity at 10^10 light year is 4.2*10-16m/s
I get a somewhat smaller figure - about 3.8×10-19m/s.
 
  • Like
Likes FactChecker
  • #14
Ibix said:
I get a somewhat smaller figure - about 3.8×10-19m/s.
Yes, you're right.
 
  • #15
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.
Does this follow?

I guess I'd have to calculate their final velocity after falling 10 million (billion!) light years.
 
  • Like
Likes FactChecker
  • #16
DaveC426913 said:
Does this follow?
Apply energy conservation:
KE + PE = const
 
  • #17
DaveC426913 said:
Does this follow?

I guess I'd have to calculate their final velocity after falling 10 million (billion!) light years.
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 other

If you assume that their velocity at that their velocity at that moment is much larger than escape velocity at that distance, then they would after separation continue to separate to an infinite distance, rather than just back out to their starting distance. Escape velocity is not only the minimum speed needed to escape to infinity, it is also the maximum speed for an object dropped (starting at rest) from an infinite distance.
 
  • Like
Likes DaveC426913 and russ_watters
  • #18
DaveC426913 said:
Does this follow?
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.

Taking 0.1kg, 0.1m apples for convenience, I get about 10 microns per second.
 
  • #19
TIL. :smile:

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)?
 
  • #20
Yes. As A.T. says, you can see it from conservation of energy, insisting that KE=0 at infinity tells you that at ground level it must be equal to the change in gravitational potential energy. And that's true going up or coming down - I've made no statement about which state was the first one.
 
  • #21
Yeah.
DaveC426913 said:
TIL. :smile:

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)?
I just realized that this is trivially true, since it's reversible.
If you send an object up from Earth at anything less than escape velocity, it will fall back (eventually), even if it takes 10,000,000,000 years. And its return velocity will be the same as its initial velocity.

Falling from infinity is merely the second half of that trajectory.
 
  • Like
Likes Ibix and phinds
  • #22
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. From energy conservation, one gets$$\frac{dr}{dt}=-\sqrt{\frac{Gm}{r_0}\left(\frac{r_0-r}{r}\right)}$$which upon integration gives the time$$T=\frac{\pi}{2}\sqrt{\frac{1}{Gm}}r_0^{3/2}=6\times10^{32}~\mathrm{years}.$$By comparison, the age of the universe is thought to be ##14\times 10^9~\mathrm{years}.##

On edit: Although the calculation for ##T## is correct for an initial separation of 10 million light years, it is not directly relevant to OP's posted distance of 10 billion years. To find the time for OP's distance, mutiply ##T## shown above by ##1000^{3/2}.##
 
Last edited:
  • Informative
  • Like
Likes Ibix and phinds
  • #23
Wow. You guys are way, way, way over my head, but it makes for some interesting reading(what I can understand of it anyway) Thanks.
 
  • #24
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.
<rant>
OHMYGOD.

Billion!
The OP's example was 10 billion light years separation!

(see post 8 if you think I'm overreacting...)
</rant>
 
  • Haha
  • Wow
Likes berkeman and FactChecker
  • #25
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>
[mea culpa]
Silly me! I looked at the wrong post when I counted zeroes. Goes to show why powers of 10 are better for expressing large numbers even in cases where the number of zeroes is no larger than the number of fingers on one's two hands. I edited my previous post to address the issue.
[/mea culpa]
 
  • Like
Likes berkeman and DaveC426913

1. What is the concept of "Gravity: Empty Universe & 2 Apples 10B Light Years Apart"?

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.

2. How does gravity affect the two apples in this scenario?

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.

3. Why is gravity considered a universal force?

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.

4. How does the strength of gravity change with distance?

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.

5. Can gravity be shielded or canceled out?

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.

Similar threads

  • Special and General Relativity
Replies
5
Views
1K
Replies
13
Views
1K
Replies
10
Views
735
  • Classical Physics
Replies
1
Views
613
  • Classical Physics
Replies
7
Views
745
  • Special and General Relativity
Replies
30
Views
2K
Replies
8
Views
1K
Replies
21
Views
2K
Replies
4
Views
1K
Replies
50
Views
2K
Back
Top