View Full Version : Quick Question

2005-Mar-02, 03:30 AM
How should I started... ok, let's put it this way, I have a friend, and currently he was taking a astronomy course which involved alots mathmatic problems. Two days ago, he offered me a question. A question about the nearby galaxy M31. This was a group project that needed to be done on next week, I think...

His question :
the andromeda galaxy is approaching us at the speed of 300 km. per sec.. if it is 2.5 million light yrs. from us,,how long will it take to collide with our own milky way galaxy??????????????

One of his partners lists out a equation : D = r x t or D = s x t
D = distance, R = Rate of speed, and T = time
Convert "light years" to "kilometer" and time to "year" do the rest...

Another one just... ahrr.. not so sure what he's trying to say... Oh here :
300 km/s is 1000 times slower than the speed of light so it will take 2.5 million times 1000 which is 2.5 billion. takes 2.5 billion years

So which person is right and which one is wrong? Or could it be both correct? :ph34r:

2005-Mar-02, 03:39 AM
The one who frustrates you is correct. He understands the problem and found the easiest solution. The speed of light is 300 000 km/sec. The 2 galaxies are coming together at 300 km/sec. Therefore, 1 light year = 1000 galaxy colision years.

2005-Mar-02, 03:52 AM
Really? Does that 2nd one works too?
Like D = 2.5 million ly, r = 300 km/sec, t = ?

2005-Mar-03, 06:44 AM
The Andromeda glaxy is approaching us at 300 km/s AT THE MOMENT. However, the force of gravity is proportional to 1/R^2. As they get closer the force of gravity increases which pulls them together with more force. This process actually requires you to know:

Current velocity, current seperating distance, mass of andromeda and milkyway. As this is non-constant acceleration you would require calculus. However actually solving this is beyond my mathematical ability.

2005-Mar-03, 10:27 PM
First, if you suppose that the speed of Andromeda Galaxy is constant and that there is no gravity, your formula D=s.t is correct and leads to 2.5 billions years... which is also the same result of the (correct) reasoning of the second person ! Good news, it's consistent.
However as pointed out by Matthew, you NEED to take the gravity into account, and you have a differential equation to solve. Should be ok if you use classical mechanics/Newton, and if you neglect the expansion oof the universe / Hubble law (as the speed is much smaller than light speed & distance small related to effect of expansion). However you need to take into account that our Milky Way also moves to Andromeda, coz the masses of these 2 galaxies are same order of magnitude. So they both converge onto their mutual Center of Gravity, in an accelerated way !

2005-Mar-03, 10:59 PM
Another thing you need to take into account is that M31 may have a velocity component coming in our direction, but it may also have a lateral velocity, that we haven't measured yet. Suppose this velocity is 50 km/sec: How long will it be till M31 and the Milky Way collide?

2005-Mar-05, 12:49 AM
Adding in the lateral velocity would just create a parabolic collision trajectory of the galaxy.

But basic phyics states that the vector components can be seperated into their two parts, in this case perpendicular and lateral components. In this case we need only consider the perpendicular compnent for the calculation.

Tim Thompson
2005-Mar-05, 01:21 AM
300 km/sec is wrong; that speed includes the local motion of Earth. The relative speed between the galaxy centers of mass, which is the speed that will determine collision time, is only 100 km/sec.

2005-Mar-15, 08:24 AM
Then again, both M31 and the Milky Way are extended objects, so the 'collision' will be when the outermost fringes of each first 'collide'. (But how do two collections of stars 'collide'? Hint: the stars don't!)