Google for "Newton Law of Gravity", then try calculating it for yourself.Me! No. I can't. That's why I asked PF.
...10,000,000,000 light years...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.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.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^{-16}m/s (assuming a 0.1 kg apple)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^{-19}m/s.The escape velocity at 10^10 light year is 4.2*10^{-16}m/s
Yes, you're right.I get a somewhat smaller figure - about 3.8×10^{-19}m/s.
Does this follow?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: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 otherDoes 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.Does this follow?
I just realized that this is trivially true, since it's reversible.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>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]<rant>
OHMYGOD.
Billion!
The OP's example was 10 billion light years separation!
(see post 8 if you think I'm overreacting...)
</rant>