Does the expansion of the Universe heat stars and bodies?

In summary: Gravity is the only force that acts on smaller systems. There is no "house pushing back" force. Gravity is the only force that acts on smaller systems. There is no "house pushing back" force.
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The expansion of space is about 68 km/s/Mpc, or 0.00002 km/s/light year. The radius of the sun is about 700000 km. Thus, initially ignoring additional forces, the change in radius of the sun due to the expansion of space is about 1.5*10^-9 m/sec, or 5 cm/year.

I assume that this expansion is real, and thus that there is a real separation of the constituents of matter. Gravitational forces acting on the less dense matter, however, will result in its collapse, which will convert the gravitational potential energy into kinetic energy, heating the system.

I don't know what the gravity profile of the sun is, but if you considered the collapse of an outer shell of the sun, having 1/4th the mass of the sun (5*10^29 kg), with surface gravity (270 m/s), moving 5 cm/yr will release about 2*10^23 W.

This is only about 0.05% of the energy from nuclear fusion (4*10^26 W), but could be more important in other bodies.

Is this reasoning flawed? The only objection I can think of is gravitational bounding means that the atomic positions do not change because some equilibrium position is found, but I don't see how that is really the case because the particles must move through space to maintain the apparent equilibrium.
 
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  • #2
Hypatio said:
Thus, initially ignoring additional forces, the change in radius of the sun due to the expansion of space is about

Sun does not expand. Expansion happens only at the scales of galaxy clusters. Smaller systems are gravitationally bound and don't expand. So your whole reasoning is based on a false premise.
 
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  • #3
weirdoguy said:
Sun does not expand. Expansion happens only at the scales of galaxy clusters. Smaller systems are gravitationally bound and don't expand. So your whole reasoning is based on a false premise.
Yes, but that is only because gravitational attraction prevents it. For every increment of expansion within the volume of the sun, there will be an increment of contraction due to gravity. If the sun actually expanded, there would be no change in internal energy, only gravitational potential energy.

Do the increments of expansion not actually occur, or do they?
 
  • #4
Hypatio said:
Do the increments of expansion not actually occur, or do they?
Within bound systems (anything the size of a galactic cluster or smaller) they do not.
 
  • #5
phinds said:
Within bound systems (anything the size of a galactic cluster or smaller) they do not.
How is it that the universe decides to expand space only outside of bound systems?
 
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Hypatio said:
How is it that the universe decides to expand space only outside of bound systems?
The universe is not a sentient being, so it doesn't "decide" anything. Expansion simply isn't strong enough to have any effect on bound systems. It's like an ant pushing on a house. It's not that the any only moves the house a tiny amount, it's that the ant doesn't move the house at all.
 
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  • #7
phinds said:
The universe is not a sentient being, so it doesn't "decide" anything. Expansion simply isn't strong enough to have any effect on bound systems. It's like an ant pushing on a house. It's not that the any only moves the house a tiny amount, it's that the ant doesn't move the house at all.
So, is the rate of expansion a function of mass within the space, or what? If the expansion of space is a constant property of space then my calculations should be correct. These are small numbers but but they are non-zero, and add up.

In the context of your analogy, the ant doesn't move the house because the house is not on a frictionless surface, so the house pushes back equally. So, where is the "house pushing back" force in the case of expansion of the universe.
 
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"Expansion of space" is a misnomer. Or an imprecision forced on you by using natural language. All that's going on is Newton's First Law, modified by curved spacetime. Distant galaxies are flying apart; that initial motion has been overcome by gravity or other forces for systems that are now bound.
 
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Ibix said:
"Expansion of space" is a misnomer. Or an imprecision forced on you by using natural language. All that's going on is Newton's First Law, modified by curved spacetime. Distant galaxies are flying apart; that initial motion has been overcome by gravity or other forces for systems that are now bound.
If expansion of space is a misnomer, I don't see it. That the motion is overcome by gravity is the concept that I am trying to apply. If gravity does not act, all mater would separate uniformly. However, gravity acts, and does so on all scales. Gravitationally unbounded systems will separate, increasing gravitational potential energy. Gravitationally bounded systems, will not separate but only because the gravitational potential energy is converted during the process of countering expansion.

I accept that I am probably wrong about this (because I've also calculated that too much heat would be produced in Earth's interior), but I do not see how I am wrong.
 
  • #10
Hypatio said:
If the expansion of space is a constant property of space then my calculations should be correct. These are small numbers but but they are non-zero, and add up.
No, it's not. @phinds ' comment is misleading, imo. What his comment does describe, is the influence of dark energy, which is a constant property of space, but that's a different effect from expansion that you can't ascertain using Hubble's law.
Using analogy to Newtonian motion, recession velocity due to expansion is like initial velocity. If you see a system with its constituents bound by their self-gravity, then it's already decoupled from expansion.
Picture expansion of the universe as a collection of objects receding from you with V0 velocities proportional to distance from your position. If those velocities are larger than the escape velocity due to the mass enclosed at a given radius, they'll keep going. If they're not, they'll stay bound. There is no force doing any work here, there's no push - just the initial velocities being sufficient or not to keep the objects moving.
 
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  • #11
Hypatio said:
Gravitationally unbounded systems will separate, increasing gravitational potential energy.
Gravitational potential is not defined in this case, so this line of argument isn't helpful. You can use it to discuss gravitationally bound systems, but it does not apply to large scale unbound systems.
 
  • #12
Bandersnatch said:
No, it's not. @phinds ' comment is misleading, imo. What his comment does describe, is the influence of dark energy, which is a constant property of space, but that's a different effect from expansion that you can't ascertain using Hubble's law.
Good point.
 
  • #13
Hypatio said:
Gravitationally unbounded systems will separate, increasing gravitational potential energy.
This is incorrect. There is no potential energy between objects at cosmological distances that are being affected by Dark Energy, only on objects where you can define a single inertial frame of reference. Energy is not conserved on cosmological scales.
 
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