Is the Solar system expanding with the Universe?

[johne1618]

Perhaps the solar system is expanding with the Universe?

For this idea to make sense one must assume that atomic lengths are constant.

The current Universal expansion rate is given by:
$$\frac{\dot a}{a} = H_0$$
where a is the current scale factor and $H_0$ is the current Hubble parameter.

Therefore we can write the approximate expression
$$\frac{\delta a}{a} = H_0 \delta t$$

Let us assume $\delta t$ is one year and $H_0$ is the reciprocal of 13 billion years.

Then in one year the Universe currently expands by the fraction $7.7*10^{-11}$.

Now the Earth-Moon distance is approximately $3.84*10^{8}$ meters.

Thus if the Solar system was generally expanding with the Universe then in a year the Earth-moon distance would increase by $7.7*10^{-11} \times 3.84*10^{8}=3$cm.

This figure is similar to the measured yearly rate that the Moon is receding from the Earth. This effect is usually attributed to tidal friction transfering angular momentum from the Earth to the Moon. But the coincidence seems intriguing to me.

Maybe one could measure this effect on a geostationary satellite which is about $36000$km from the center of the Earth?

In this case Universal expansion would cause the orbital distance to increase by $7.7*10^{-11} \times 3.6*10^{7}=3$mm a year.

This should be measureable?

I guess the problem is that other effects such as changes in the solar wind, radiation pressure, variations in the Earth's gravitational field, and the gravitational effect of the Moon and Sun would mask any Universal expansion effect.

 

[Mordred]

There have been proposols that expansion causes slight widening of orbits. Here is an article conveying that

http://arxiv.org/abs/gr-qc/0602098

 

[bapowell]

Your expression $H = \dot{a}/a$ is for an FRW universe. Is the solar system well-described by the FRW solution?

 

[Naty1]

Bapowell has the right idea... he knows neither the solar system nor our Milky Way galaxy does NOT fit an FRW cosmological model...

The FLRW model [for a homogeneous and isotropic universe as an approximation for our universe] does NOT apply at galactic distances...too much lumpiness.

Nobody knows how to solve the EFE for representative galactic conditions...how to include the lumpiness, in other words. So we should say something like ‘gravitationally bound systems [solar systems galaxies,etc] and things inside them are not thought to expand [or are generally not considered to expand] but we have no exact solution for such conditions.

However you like to word it, the balloon analogy correctly recognizes fixed solar system or galaxy sizes via 'pennies'...which do not expand as the the balloon surface is inflated...rather than,say, ink circles...which would expand along with the balloon expansion.

 

[Chronos]

The universe has only expanded by about 7.5% in the past billion years. While that happens to be close to the average recession speed of the moon over the past billion years, the reasons are unrelated.

 

[johne1618]

The universe has only expanded by about 7.5% in the past billion years. While that happens to be close to the average recession speed of the moon over the past billion years, the reasons are unrelated.

As a matter of interest, how does the orbital speed of the moon change with time?

Has it been measured?

Presumably if the Moon is in orbit then the square of its orbital velocity should be inversely proportional to its distance from the Earth. Thus if the distance is increasing then one would presume its orbital velocity is decreasing.

 

[Chalnoth]

Perhaps the solar system is expanding with the Universe?

Nope. To examine this, what is generally done is to consider the perturbed FRW equations. Here what is done is to ask the question about what happens if you have variations in density from place to place. And one of the fundamental results is that if you have an overdense region that is small enough, as long as there is no dark energy, its size is constant with time.

So there may be some small instability in our solar system due to dark energy, but dark energy itself is so tiny that no, we haven't been able to measure its effects within our solar system.

 

[Naty1]

Perhaps the solar system is expanding with the Universe?

not for the reasons cited so far...but it could change slightly due to other more mundane factors...like emission of gravitational wave energy, changes in position of the Milky Way and Andromeda galaxies, burning off mass from our sun, increased size of our Milky Way supermassive black hole, offset maybe by accumulating space debris here on earth...etc,etc...