# How can I calculate distances between stars?

*I am in 10th grade and consider myself a fairly competent amateur astoronomer.
I am doing a project on distribution of certain objects using some of the
newish redshift data, I have been looking and looking for a formula that I
could use to change RA, DEC and distance to X,Y and Z. I want to do this so
that i can measure distances from one object to the next which I can't do
unless i put the objects on a coordinate grid.*

In mathematics and physics, we don't only use cartesian coordinates (x,y, and z). For some kind of problems we use other kinds of coordinate systems. In your case, the natural coordinate system to use would be 'spherical coordinates'. You can look at the web page: http://mathworld.wolfram.com/SphericalCoordinates.html, and I will tell you how to relate these coordinates to your problem. (by the way, if you don't know this webpage yet, it is a reliable source of information about math).

In spherical coordinates, you have 3 coordinates, just like you have x, y and z in cartesian coordinates. These coordinates are: r, which is the distance between the origin and a point, and then two angles that work just like latitude and longitude on Earth, or as RA and DEC in the sky.

So if you want to apply these to your objects you have to set r as the distance to the object (which you get from its redshift, as you know). Then 'theta' is the azimuthal angle, which means it is your RA. But watch out! RA is generally given in units of hours,minutes, and seconds, which you will have to convert to decimal degrees. And finally, the 'phi' angle is your DEC. But once again, if your declinations are in degrees, minutes and seconds, you will need to convert them to decimal degrees. DEC goes from 90 degrees at the north celestial pole to -90 at the south celestial pole, but you need to have 'phi' from 0 to 180 degrees, so you should do " phi=90degrees-DEC ".

Now all your objects should be described by these coordinates. But to measure distances between them, the easiest for you might be to convert these coordinates to standard x,y, and z coordinates, and then calculate distance as usual. If you go to the web page I told you about before, you will get formulas to go from r, theta and phi to x, y, and z (equations 4, 5, and 6 as they number them). This should do the trick for you!

Good luck with your project!

# Still Curious?

**Get More 'Curious?' with Our New PODCAST:**

- Podcast? Subscribe? Tell me about the Ask an Astronomer Podcast
- Subscribe to our Podcast | Listen to our current Episode
- Cool! But I can't now. Send me a quick reminder now for later.

**Related questions:**

- What are RA and DEC?
- Why don't astronomers use everyday units to measure distances (what is an AU or a pc)?

**More questions about Stars:** Previous | Next

# How to ask a question:

If you have a follow-up question concerning the above subject, submit it here. If you have a question about another area of astronomy, find the topic you're interested in from the archive on our site menu, or go here for help.

Main Page | About Us | For Teachers | Astronomy Links | Ask a Question | View a Random Question | Our Podcast

Table 'curious.Referrers' doesn't existTable 'curious.Referrers' doesn't existURL: http://curious.astro.cornell.edu/question.php?number=302

This page has been accessed *31713* times since October 9, 2002.

Last modified: *October 29, 2004 1:26:50 PM*

Ask an Astronomer is hosted by the Astronomy Department at Cornell University and is produced with PHP and MySQL.

**Warning: Your browser is misbehaving! This page
might look ugly.** (Details)