# Orbital distance

1. Mar 14, 2005

### iamsomeguy

Is there a resource showing relative distances between the planets charted for different times of the year?

Specifically, I'm looking for tables or software where I can type in a date, and a starting location, say Mars, and see the distance to a selected body in the solar system, say Jupiter.

For example:
I can select my starting location to be Venus, my date to be March 10, 2005 and my destination to be Saturn. Then it will give me the distance between the two.

Thank you.

2. Mar 14, 2005

### chroot

Staff Emeritus
Welcome to PF, iamsomeguy.

I spent some time looking on the web, but couldn't find any sites that already do exactly what you're looking to do. Fortunately, it's really not all that complicated. The hard part is simply finding the data. First, I'll give you three different methods for finding such data:

1) Here's a nifty little Excel macro package that can calculate the positions of the planets. You just plug the macros into Excel, then use simple functions to perform the calculations. http://www.xylem.f2s.com/kepler/astrofnc.html [Broken]

2) I use a wonderful little program called XEphem for astrometric calculations. XEphem produces decent star charts, but its real value is its flexibility in getting data into or out of it. It's free software, but the downside is that it's a Unix program. If you're using Windows, you can still use XEphem, but you'll need some technical savvy. You can first install the Cygwin package (which provides a Unix-like environment for Windows), then compile XEphem on top of Cygwin. http://www.clearskyinstitute.com/xephem/

If you're willing to pay money for a program, I believe two of the most popular packages, Starry Night Pro and TheSky, are both easily capable of making these calculations.

3) You can calculate the numbers yourself with a calculator or small computer program, using some of the algorithms detailed at these websites:

http://www.stjarnhimlen.se/comp/tutorial.html
http://www.stjarnhimlen.se/comp/ppcomp.html

You can use any of the three methods above to get three spherical coordinates for each planet: the heliocentric latitude, longitude, and distance. With these coordinates, it's a simple matter to calculate distances.

I don't know your level of math or computer skills, so let me know if you need additional help.

- Warren

Last edited by a moderator: May 1, 2017
3. Mar 14, 2005

### tony873004

You can get the distances between any 2 solar system objects, including all planets, most moons, hundreds of thousands of asteroids & comets, and lots of spacecraft by sending an e-mail to JPL Horizons at the following address:
horizons@ssd.jpl.nasa.gov

put the word job in the subject line

and a modified version of this in the body:

!$$SOF EMAIL_ADDR='' START_TIME = '2029-Apr-01 00:00:00' STOP_TIME = '2029-Apr-01 00:00:01' TABLE_TYPE = 'Vector' REF_PLANE = 'Ecliptic' CENTER = '@010' COMMAND='199' !$$EOF

Change your start time and stop time to whatever you want. Notice that stop time is 1 second more than start time.

in Center =
you need the @ sign, then put in an object id

in Command =
you just need the object id

both need to be in single quotes

Object id list:

010: Sun
199: Mercury
299: Venus
399: Earth
etc,ect...
999: Pluto

301: Earth Moon
401 & 402: mars moons
501-5xx: Jupiter Moons, etc

For a complete list, visit the JPL Horizons web page.

So in the above example, I asked for Mercury with respect to the Sun. Horizons automated system took less than 20 seconds to send me a reply e-mail that contained the following data:

*******************************************************************************
$$SOE 2462227.500000000 = A.D. 2029-Apr-01 00:00:00.0000 (CT) 3.983419164516005E+07 2.717340591298079E+07 -1.432368585167380E+06 -3.700246350807901E+01 4.235721524755920E+01 6.855282109693581E+00 1.609151534147640E+02 4.824114937165917E+07 -6.898523657281064E+00$$EOE
*******************************************************************************

Notice the numbers I boldfaced. They are the x-component of the distance, the y-component of the distance, and the z-component of the distance expressed in kilometers. The next 3 numbers are velocity components.

from these numbers, you can come up with a distance
$$d=\sqrt {x^2+y^2+z^2}$$
which equals 48241149.3716592 kilometers in the above example.

4. Mar 14, 2005

### chroot

Staff Emeritus
tony,

Excellent resource! Thank you!

- Warren

5. Mar 15, 2005

### tony873004

Thanks.

Here's a link to a program I wrote that creates the text of the e-mail for you. You can select from almost 200 solar system objects in the dropdown lists so you don't have to refer to things by their ID numbers.

Ignore page 2 of the calculator (unless you use Orbiter). It wants you to paste the reply e-mail into it, then it searches it for the data it needs to create output that can be used in the program Orbiter -- Space Flight Simulator to properly position the object.

But for this purpose, its still easier since it gives you lists, and computes the stop date for you.

orbitsimulator.com/orbiter/cfgData.exe

6. Mar 16, 2005

### iamsomeguy

Thank you all for your help.

Tony, the link you provided (orbitsimulator.com/orbiter/cfgData.exe) doesn't seem to work. I am also unable to get to the site by it's IP (207.150.192.12). Is your server down?

It's been a long time since I did any real math. For 3d distances isn't it D=SQRT((x1-x2)^2 + (y1-y2)^2 + (z1-z2)^2)

Also, I noticed the spreadsheet, an excellent resources btw, doesn't have Earth on it

7. Mar 16, 2005

### tony873004

Your formula is right, but the data from Horizons is actually giving you x1-x2, ie position x of the sun - position x of mercury, so that part is done for you. Or you could look at it like position x,y,z sun (or whatever object has the @ sign in front of its ID number) is always 0,0,0, so the position for mercury is 0- xyz positions for mercury. The - signs go away as you square them.

The link seemed to work for me. I just tried it. Try it again. Maybe the server was down at that moment or slow. Maybe your browser's security levels prevent you from downloading executables.

8. Mar 17, 2005

### iamsomeguy

Thank you.

The resources provided are incredible and I'm grateful for all your help.

And, I give thanks for Excel

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