Formulas for Elliptical Orbits X,Y,Z Co-Ordinates

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In summary, the conversation is about someone asking for the formulas for calculating the x, y, and z coordinates of a planet on its elliptical orbit around the sun. They mention being open to using astronomy terms and asking for a tutorial or paper to help. The conversation ends with someone suggesting looking up terms such as true anomaly, elliptical anomaly, mean anomaly, Kepler's equation, and orbital elements as a starting point.
  • #1
frogtag
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Can someone tell me what the formulas are for the x,y & z co-ordinates of a planet on its elliptical orbit of the sun?

I don't mind astronomy terms (I'm no expert on them but have a basic knowledge and will look up and learn any I don't know).

It's not homework, just something that's doing my head in!

A tutorial or paper would help if that's less writing for you?

Thank you.
 
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  • #2
I have to leave for the airport in a short time, so no time for a write-up. However, google these terms:
- true anomaly
- elliptical anomaly
- mean anomaly
- Kepler's equation
- orbital elements
 
  • #3
Cheers this is a good starting base for me.
 

Related to Formulas for Elliptical Orbits X,Y,Z Co-Ordinates

1. What are the formulas for calculating X, Y, and Z coordinates in an elliptical orbit?

The formulas for calculating X, Y, and Z coordinates in an elliptical orbit are:

X = a * (cos(E) - e)

Y = b * sin(E)

Z = 0

Where a is the semi-major axis, e is the eccentricity, and E is the eccentric anomaly.

2. How do I determine the semi-major axis of an elliptical orbit?

The semi-major axis of an elliptical orbit can be determined using the following formula:

a = (r1 + r2) / 2

Where r1 and r2 are the distances from the center of the ellipse to the two foci.

3. What is the difference between the eccentricity and the eccentric anomaly?

The eccentricity (e) is a measure of how elliptical an orbit is, while the eccentric anomaly (E) is an angle that describes the position of an object in its orbit relative to the center of the ellipse.

4. Can I use these formulas for any type of elliptical orbit?

These formulas are specifically for calculating X, Y, and Z coordinates in a Keplerian elliptical orbit, where the orbiting body is subject to the gravitational force of a single central body. They may not be accurate for other types of elliptical orbits, such as those affected by multiple gravitational forces or other external forces.

5. How accurate are these formulas?

The accuracy of these formulas depends on the accuracy of the input parameters, such as the semi-major axis and eccentricity. In general, they provide a good approximation for calculating X, Y, and Z coordinates in an elliptical orbit, but for more precise calculations, more complex formulas and methods may be necessary.

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