# Converting/Creating Coordinate Systems for Other Planets?

• Raymond_
In summary, the individual is trying to develop coordinate systems for other planets to visualize the sky and its stars from a given location. They have been reading various resources but still have some confusion. The suggested method is to use vector calculus to find axis directions for the planet and its orbit, and then convert from ecliptic to equatorial coordinates. This will allow for the conversion of an object's position from Earth equatorial coordinates to the planet's analog of right ascension and declination.

#### Raymond_

Hi, this may be a very basic concept, but I'm trying to develop coordinate systems for other planets from their right ascension and declination and prime meridians so that, given a location on that planet, you could visualize the sky and its stars.. I've been reading http://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE2009reprint.pdf and some wiki pages, but I'm pretty new to astronomy and am pretty confused :( . I know stellarium has the functionality to do this, and if anyone could explain how they do it or give me some further reading/clear explanations, I'd really appreciate it. Thanks for any help!

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I'm not quite sure what you're wanting to do. Are you wanting to view the sky as it is seen by an observer on another planet?

Yup, that's exactly what I'm trying do (sorry for wording it unclearly), but as I understand it, you have to create a coordinate system for every planet, right?

Hmmm. I'm not sure. Sorry I can't be of much help.

That's okay, thanks anyways :/ let me know if you know of any helpful links that could potentially help me muddle through this. Thanks!

It seems like you want to create another planet's analog of the Earth's right ascension and declination.

I think that the easiest way to do it is with vector calculus. Spherical trigonometry is mathematically equivalent, but it's a nightmare to keep it straight.

You will need to find axis directions X, Y, Z for the planet. Z is the direction of the planet's north pole, X is the direction of its vernal equinox, and Y forms a right-handed triplet with those two: Y = (Z)x(X).

For that, you will need the directions of both the planet's north pole and its orbit's north pole in Earthly coordinates.

The planet's north pole is simple. You can usually find it as right ascension (α) and declination (δ), the celestial version of Earthly longitude and latitude.
$$Z(planet) = \{ \cos \delta \cos \alpha, \cos \delta \sin \alpha, \sin \delta \}$$
The orbit's north pole is more complicated. It's often given in the Earth's ecliptic coordinates, and indirectly, from the orbit's inclination and ascending-node longitude.
$$Z(planet-orbit) = \{ \sin i \sin \Omega, - \sin i \cos \Omega, \cos i \}$$
To get from the Earth's ecliptic coordinates to its equatorial ones, you need the Earth's obliquity ε:
$$X(ecliptic) = \{1, 0, 0 \} ,\ Y(ecliptic) = \{0, \cos\varepsilon, \sin\varepsilon \}, Z(ecliptic) = \{0, -\sin\varepsilon, \cos\varepsilon \}$$
To get from ecliptic to equatorial coordinates, you must do
$$Z(PO-equatorial) = Z(PO-ecl,1) X(ecliptic) + Z(PO-ecl,2) Y(ecliptic) + Z(PO-ecl,3) Z(ecliptic)$$
where the 1, 2, and 3, are the three components of Z(PO-ecl) = Z(planet-orbit-ecliptic).

Once you have that, then
$$X(planet) \sin\varepsilon(planet) = Z(planet-orbit) \times Z(planet) ,\ Y(planet) = Z(planet) \times X(planet)$$

So the position in planet coordinates of an object at position n in Earth equatorial coordinates is {n.X(planet), n.Y(planet), n.Z(planet)} and it can be converted to the planet's analog of right ascension and declination if one so desires.

## 1. What is a coordinate system?

A coordinate system is a mathematical system used to determine the position or location of a point in space. It is typically made up of a set of axes, reference point, and units of measurement.

## 2. Why do we need to convert/ create coordinate systems for other planets?

Each planet has a unique shape, size, and orientation in space, which makes it necessary to have specific coordinate systems to accurately represent and measure positions on that planet's surface. Converting or creating coordinate systems ensures that data collected from different planets can be compared and analyzed correctly.

## 3. How are coordinate systems created for other planets?

Coordinate systems for other planets are created by using data from spacecraft observations, ground-based telescopes, and mathematical models. Scientists use this information to define the shape, orientation, and reference points for a planet's coordinate system.

## 4. What are the challenges in converting/creating coordinate systems for other planets?

One of the main challenges is accurately determining the shape and orientation of a planet, as well as identifying reference points that can be used for measurements. Another challenge is ensuring that the coordinate system is compatible with existing systems to facilitate data sharing and analysis.

## 5. Can coordinate systems be used for all objects in space?

No, coordinate systems are unique to each object in space and cannot be used interchangeably. This is because each object has its own shape, size, and orientation, and therefore requires its own coordinate system for accurate measurements.