Hubble Law - recession velcoity?

[jsmith613]

Hubble Law - recession velcoity?

v = H₀d tells us that the recession velcotiy of a galaxy is directly related to its distance from us on earth

However, as the planets move further apart, their potential energy increases (and hence kinetic energy decreases).

How do these two phenomena tie together?

 

[axemaster]

Well, there's a couple of things I'd point out here.

First, kinetic and potential energy don't necessarily imply that the velocity of a further away object should be lower on an immediate basis. They only imply that it should slow down as it moves away, in a continuous exchange of energy.

In general we expect that most objects should come out of the Big Bang with roughly the same energy, but spread out all over the place. So you can imagine a condition where everything in the universe is stationary, and nothing moves (thus killing your energy argument).

Now add the expansion of space-time. This causes an anomalous change in the velocity, equal to that given by Hubble's law. Objects further away move faster because there is more expanding space between you and them (you can see why the relationship would be linear). But it doesn't affect the energy balance because objects are still stationary with respect to their own local space.

Does this make any more sense?
Edit: I know this example has been done to death, but imagine a partially filled balloon, with 2 dots on the surface. The dots may or may not be moving on the surface of the balloon - this is their energy. Now blow up the balloon, and they move apart. The dots move apart because they are anchored in their local spacetime, which is expanding. But that expansion doesn't affect their velocity within their spacetime.

 

[jsmith613]

Well, there's a couple of things I'd point out here.Does this make any more sense?

so your saying I cannot compare the two situations.
It is the space that is expanding and they, being attached the space, therefore move with it.

but PE must be increasing between planets so where is this energy from?

 

[Drakkith]

so your saying I cannot compare the two situations.
It is the space that is expanding and they, being attached the space, therefore move with it.

While a very common way of explaining the expansion of the universe, objects are not actually "attached" to space. The math in General Relativity that we use to calculate all this is very complicated, but it turns out that objects not bound to each other simply get further apart as time passes. At least, that is how I understand it.

but PE must be increasing between planets so where is this energy from?

It already had the energy in the form of kinetic energy. Let's look at something such as a comet with a very high eccentric orbit where its closest approach is 1 AU and it's furthest is 10 AU. As the comet moves from 10 AU towards the Sun, it's potential energy is converted into kinetic energy until it reaches it's closest point to the Sun at 1 AU, at which point it will have attained it's maximum velocity. As it moves back out to 10 AU the kinetic energy is converted back into potential energy as the comet loses speed and gains distance. At 10 AU the comet will have it's slowest velocity and it's most potential energy.

 

[Steely Dan]

It already had the energy in the form of kinetic energy. Let's look at something such as a comet with a very high eccentric orbit where its closest approach is 1 AU and it's furthest is 10 AU. As the comet moves from 10 AU towards the Sun, it's potential energy is converted into kinetic energy until it reaches it's closest point to the Sun at 1 AU, at which point it will have attained it's maximum velocity. As it moves back out to 10 AU the kinetic energy is converted back into potential energy as the comet loses speed and gains distance. At 10 AU the comet will have it's slowest velocity and it's most potential energy.

This is true, but not really a proper analogy. The gravitational potential energy of the Universe (if such a concept has meaning) is clearly increasing with time, if it is true that the distance between all galaxies grows farther apart with time. This does not imply that this is made up for in reduced kinetic energy of the galaxies: clearly, if we can even define kinetic energy for a galaxy at a cosmological distance, it must be increasing with time as well, since it is gaining speed with time. There is no requirement that our universe abide by energy conservation on a global level, so there is not necessarily a paradox here.

 

[Drakkith]

This is true, but not really a proper analogy. The gravitational potential energy of the Universe (if such a concept has meaning) is clearly increasing with time, if it is true that the distance between all galaxies grows farther apart with time. This does not imply that this is made up for in reduced kinetic energy of the galaxies: clearly, if we can even define kinetic energy for a galaxy at a cosmological distance, it must be increasing with time as well, since it is gaining speed with time. There is no requirement that our universe abide by energy conservation on a global level, so there is not necessarily a paradox here.

Isn't the OP talking about planets? (Granted he is referring to hubbles law, but that doesn't apply to planets)

 

[Steely Dan]

Since he specifically mentioned Hubble's law, I assume by "planets" he meant galaxies or whatever.

 

[jsmith613]

Isn't the OP talking about planets? (Granted he is referring to hubbles law, but that doesn't apply to planets)

I meant galaxies...Hubble's law only works for galaxies.

But how can E_k and E_p both increase?

 

[SHISHKABOB]

I meant galaxies...Hubble's law only works for galaxies.

But how can E_k and E_p both increase?

like steely dan said, conservation of energy on a "universal" level is not necessary

 

[Chronos]

Hubbles law applies to the metric of spacetime, it has nothing to do with atoms, planets, stars, galaxies, or even clusters of galaxies.