# What is the position and orientation of the Earth as a function of time

I would like to know the position and orientation of the Earth, relative to the sun, as a function of time.

I.e. select any coordinate system with the Sun at the origin so that the earth lies in the x-y coordinate plane. Provide a function which takes as input the time and produces

1. The x-y position of the center of the Earth
2. The unit vector from the center of the Earth to the North Pole.
3. The orientation of the Earth around this vector

This function is chaotic in general. I would be happy with a decent approximation.

This problem is solved as part of the "what is the position of the sun in the sky" problem. Solutions to this problem tend not to be well separable (at least I have trouble separating my question out of the complete position-of-sun-in-sky solution.)

• What precision? How broad is the time domain? First approximation is cosine, sine, and constant. – Andrew Apr 10 '12 at 11:35
• Ha, yes, I suppose that would satisfy the posed question. I'd like the same precision/range present in solutions to position-of-sun-in-sky problems. Mostly I just want this part of that solution to be cleanly separated out. – MRocklin Apr 10 '12 at 12:01
• Why the down-vote? Please help by informing me how I can make the question more clear. – MRocklin Apr 13 '12 at 16:53
• It wasn't me, but I'd guess it was the same lack of precision as my comment asked about. You could ask, "What is the dominant correction term to the cosine, sine, constant approximations." – Andrew Apr 13 '12 at 20:51