# The expanding universe isn't in our neighborhood

1. Sep 9, 2009

### bwana

The 'measurement' of the radial expansion of the moon's orbit is 3.8 cm/yr
http://curious.astro.cornell.e...uestion.php?number=124 [Broken]

but that measurement is only slightly more than the hubble constant
(the rate that the universe is expanding)

Here is my calculation:
Hubble expansion
=70.8 km/sec / Megaparsec
=70.8 km/sec / 3.08x 10^19 km
= 2.3 km/sec / 1 x 10^18 km
= 2.3 m/s / 1 x 10^18 m

moon's radial expansion / dist to earth
3.8x10^-2 m/yr / 4 x 10^5 km
yr=365x24x60x60 sec
3.8x10^-2 m/3.15x10^7 sec / 4 x 10^5 km
3.8x10^-2 m/s / 1.26 x 10^13 km
3.8 m/s / 1.26 x 10^15 km
3.02 m/s / 1 x 10^18 m

The radial expansion of the moon was measured using the cube mirrors left by Apollo on the moon. Very simple. ---didnt they really just measure the Hubble constant? Isnt the moon really just moving away much more slowly than we measured because of the hubble constant? Well, everyone seems to agree that the moon's orbit is expanding and this energy is equal to the energy lost by a decreasing rotational velocity of the earth. So why isnt space expanding in our neighborhood since we do have the ability to detect it?

The argument goes that gravity keeps stuff together in our neighborhood. Simply put to me has been the following explanation by another more erudite scholar:

Think of expanding space like a dynamically sizable swimming pool. Gravitationally bound objects are then represented by objects in the pool that are connected by strings. The string representing the gravitational attraction each body has on the other keeping them together. Now let's grab the sides of the swimming pool and stretch out the pool by twice it's original size. The objects that are gravitationally bound don't fly apart (the strings keep them together). Those that are not gravitationally bound though will move apart.

But I see a problem with this explanation.

If space is expanding, then this imparts energy to all celestial bodies. Simply put, if you have velocity,X, but all distances are increasing by delta, then your velocity is really x+delta. But we do not detect the velocity increase(even though we could)-Notice I did'nt say anything about gravity in the above example. I am just talking about a random body in space, like a comet. This violates Newton's law-that an object in motion stays in the same motion. Here is an interesting calculation:

Given that velocity increase is proportional to distance (Hubble's Law), the following calculation shows how velocity should increase over time.

Distance(D)=velocity(V)*time(t)
∂D=V*∂t
and we also know Velocity=Hubble constant*distance, V=H*D

∂D=H*D*∂t
∂D/D=H*∂t
Integrating both sides:
Ln(D)=H*t + C where C is a constant
Distance = e^((H*t)+C)

Exponential increases in distance are not seen though SO we are claiming that gravity prevents this. From what others have said, gravity keeps the spatial arrangement constant-various analogies were proposed-the swimming pool for example.

So, people holding hands in a radially expanding pool would feel a current pushing them apart. This 'centrifugal' acceleration occurs without them moving in a circle-they just have to stand there. This is like an apple keeping a string taught without having to spin it.

But this runs counter to our observations in the real world as well. Without orbital motion, celestial bodies are attracted and fall toward each other, no matter how small they are-even a space capsule cannot remain at a fixed distance above the earth without motion. So, the explanation is that the expansion of space is prevented in a gravity well-not that the celestial bodies are constrained.

Another confirmation would be to look in an intense gravity well (like a black hole). Is Hubble's law not seen in the regions of quasars?

Last edited by a moderator: May 4, 2017
2. Sep 10, 2009

### Chronos

Recession of the moon is readily explained by newtonian gravity, no need to invoke the hubble flow.

3. Sep 10, 2009