# What's the acceleration of our galaxy? (1 Viewer)

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#### Lucretius

I know that the velocity of our galaxy towards Andromeda is approximately 300,000km/s, but how quickly does this velocity change? Or can we tell given our relatively short time observing the sky?

#### jcsd

Gold Member
Acceleration requires a force, which force is acclerating the Milky Way towards Andromeda? The only force that could conceivably be signifcant is gravity.

A simple back of the envelope caluclation (pretty rough and ready, could easiy be an order of magnitude out), reveals the acceration due to the Andromeda galaxy's gravity of the Milky Way is approx. 3 x 10^-21 ms^-2.

#### vincentm

jcsd said:
Acceleration requires a force, which force is acclerating the Milky Way towards Andromeda? The only force that could conceivably be signifcant is gravity.

A simple back of the envelope caluclation (pretty rough and ready, could easiy be an order of magnitude out), reveals the acceration due to the Andromeda galaxy's gravity of the Milky Way is approx. 3 x 10^-21 ms^-2.
I believe the velocity that the Andromeda galaxy is accelerating towards the Milky Way is 50 kilometers a second, i could be wrong though.

#### jcsd

Gold Member
vincentm said:
I believe the velocity that the Andromeda galaxy is accelerating towards the Milky Way is 50 kilometers a second, i could be wrong though.
The acceleration would be approximately half what I quoted above for the Milky Way (i.e. alot less than 50 km/s^-2).

btw I just checked Lucretius's original figure, the two galaxies are travelling towards each other at 300,000 mph rather than 300,000 km/s.

#### SpaceTiger

##### Only Cat With a Helmet
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Gold Member
Lucretius said:
I know that the velocity of our galaxy towards Andromeda is approximately 300,000km/s
jcsd already noted this, but that's much too large. 300,000 km/s is the speed of light.

the acceration due to the Andromeda galaxy's gravity of the Milky Way is approx. 3 x 10^-21 ms^-2.
Are you just using Newton's law of gravity? If so, what numbers are you using? With 1012 solar masses for Andromeda and a megaparsec separation, I'm getting it to be about a factor of a billion less:

$$a \sim 10^{-13}~m/s^2$$

My number is more like what I would expect, since accelerating at that rate for the age of the universe produces a velocity:

$$v \sim at_u \sim (10^{-13}~m/s^2)(10^{10}~years) \sim 100~km/s$$

which is of the same order of magnitude as the current velocity between the galaxies.

Also, I think it's worth mentioning that the masses of the Milky Way and Andromeda galaxies are still very uncertain, so estimates of the acceleration would be as well.

BTW: The unit calculator in my signature makes these calculations a lot easier.

K

#### Kino

##### Guest
In the book "The Alchemy of the Heavens" by Ken Croswell it states that the Andromeda galaxy approaches the Milky Way 6.4 million miles (10.4 Mkm) every day.

I think we can assume that the acceleration is extremely small and a velocity of 100 km/s would achieve 8.6 Mkm. A reasonably good agreement.

In answer to the first post: the acceleration won't change, but the velocity will. This could be determined by the change in blue-shift (as it is approaching us).

#### jcsd

Gold Member
SpaceTiger said:
jcsd already noted this, but that's much too large. 300,000 km/s is the speed of light.
You know what I didn't even notice it was the speed of light (anything other than SI units just don't mean anythign to me even when the conversion is trivial)!

Are you just using Newton's law of gravity? If so, what numbers are you using? With 1012 solar masses for Andromeda and a megaparsec separation, I'm getting it to be about a factor of a billion less:

$$a \sim 10^{-13}~m/s^2$$

My number is more like what I would expect, since accelerating at that rate for the age of the universe produces a velocity:

$$v \sim at_u \sim (10^{-13}~m/s^2)(10^{10}~years) \sim 100~km/s$$

which is of the same order of magnitude as the current velocity between the galaxies.

Also, I think it's worth mentioning that the masses of the Milky Way and Andromeda galaxies are still very uncertain, so estimates of the acceleration would be as well.

BTW: The unit calculator in my signature makes these calculations a lot easier.

I used 2.5 million light years and 12 x 10^12 solar masses, so yes I have made an error in my caculation (I used google cacualtor to convert the units and windows calcualtor to calculate).

#### Janus

Staff Emeritus
Gold Member
Kino said:
In answer to the first post: the acceleration won't change, but the velocity will. This could be determined by the change in blue-shift (as it is approaching us).
Actually, the acceleration will change. As the two galaxies draw closer together, the force of gravity between them will increase. So when the distance between them has halved its present value, that value of $a \sim 10^{-13}~m/s^2$ will have increased by a factor of four.

#### vincentm

Is Andromeda moving towards us, or are we moving towards it? I think it's both moving towards eachother, right?

#### Ophiolite

It's all relative.

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