Calculate the distance of a Hydrogen cloud given its velocity

[Ben231111]

Homework Statement

Using a radio telescope we are recording data from the galactic plane at the 1420.4MHz frequency of neutral Hydrogen - we are aiming to create a polar map of the Hydrogen in the Milky Way. When looking through a cloud of Hydrogen (i.e. a spiral arm) the frequency observed can be doppler shifted depending upon the relative velocity of the cloud, this allows us to calculate the velocity of the cloud along our line of sight. Now all we need is to calculate the distances of these observed clouds. We know the distance from us to the centre of the galaxy, we know the longitude of the cloud (angle between the galactic centre, us and the cloud), we know the velocity of the Sun around the Milky Way and we know the observed velocity of the cloud along the line of sight. How can we calculate the distance to the cloud? We think this is just a geometry problem but we may be wrong.

Homework Equations

Trig equations

The Attempt at a Solution

We can calculate the distance from the centre of the galaxy to the closest point of the line that runs through the Sun and this cloud somewhere else in the galaxy (so where this line is perpendicular the centre of the galaxy). We have tried using all the tricks in the book geometry wise and have come up short to how to find the solution. Any ideas?

 

[mfb]

You cannot determine the distance without further assumptions.
Is the cloud in the galactic plane, and rotating with some speed that depends on its position in a known way?
If yes, you can set up an equation for that (using some input from astrophysics), and then find the right distance where the velocity matches observations.

 

[Ben231111]

You cannot determine the distance without further assumptions.
Is the cloud in the galactic plane, and rotating with some speed that depends on its position in a known way?
If yes, you can set up an equation for that (using some input from astrophysics), and then find the right distance where the velocity matches observations.

Thanks for the reply mfb. We are indeed assuming that the velocities of the Sun and the cloud are the same (although we have only observed the velocity of the cloud along the line of sight) - this is due to the rotation curve of the Milky Way being approximately constant due to the extra matter in the form of dark matter.