Orbital Mechanics: need spreadsheet for Earth's location every minute

[neomagik]

Hi,


I am working on a 3d model of the earths orbit around the sun, to perfect scale.


I know you can compute the 3 necessary anomaly angles to determine the position but what I need is a spreadsheet that can compute the cartesian XYZ coordinates of the earth position for any given minute of a specific year using the eccentricity value of the elliptical orbit and the axes lengths at perihelion and aphelion for that particular year.


I realise that the spreatsheet will be huge (accounting for every minute of an entire year) but I have a script that allows me to copy/paste XYZ coordinates and will draw the path in my 3d software automatically. Any formula needs to assume that the sun is at the coordinates 0,0,0 with the earth being at a negative x value (9 o'clock position) in January at the perihelion, moving counter-clockwise.


Any assistance with a suitable spreadsheet would be gratefully received.


Thanks

 

[Deleted member 4993]

Hi,


I am working on a 3d model of the earths orbit around the sun, to perfect scale.


I know you can compute the 3 necessary anomaly angles to determine the position but what I need is a spreadsheet that can compute the cartesian XYZ coordinates of the earth position for any given minute of a specific year using the eccentricity value of the elliptical orbit and the axes lengths at perihelion and aphelion for that particular year.


I realise that the spreatsheet will be huge (accounting for every minute of an entire year) but I have a script that allows me to copy/paste XYZ coordinates and will draw the path in my 3d software automatically. Any formula needs to assume that the sun is at the coordinates 0,0,0 with the earth being at a negative x value (9 o'clock position) in January at the perihelion, moving to a 6 o'clock position (-x and -y) etc etc


Any assistance with a suitable spreadsheet would be gratefully received.


Thanks

When you say perfect scale:

Radius of sun ~ 400 K miles

Radius of earth ~ 4 K miles

Average distance of earth from sun ~ 93,000 K miles

These can create huge problem in scaling. However, the orbit of earth has an eccentricity of less than 0.02 (Very very very close to circle). Thus the tilt of earth is more important than eccentricity in effect of sun on earth.

 

[neomagik]

When you say perfect scale:

Radius of sun ~ 400 K miles

Radius of earth ~ 4 K miles

Average distance of earth from sun ~ 93,000 K miles

These can create huge problem in scaling. However, the orbit of earth has an eccentricity of less than 0.02 (Very very very close to circle). Thus the tilt of earth is more important than eccentricity in effect of sun on earth.

I mean perfectly to scale.

The units are km. I have the earth drawn at a radius of 6.371 (all my km values are divided by 1000 to function in the 3d software) I have the earth tilted at 23.44 degrees and spinning at the exact rate.

I know this is possible as I have written a script in AutoCAD which takes the distance from the earth to the sun for each minute as provided by NASA and draws a circle of corresponding radius centred on the sun. The point at which the circle intersects the ellipse (drawn using the eccentricity value and aphelion and perihelion distances) is the position of the earth on the ellipse. I have then extracted these intersection coordinates as XYZ coordinates (only X and Y are needed really) and then imported them in to the animation software. The results are very good. The day/night terminator line and position of the moon is very accurate including moon phases when I add light from the sun and animate the model.

The trouble I'm having is that my AutoCAD script is limited in character length and besides, AutoCAD struggles to process more than about 300 circles (or minutes)

This is why I need a spreadsheet to calculate the positions (as XYZ coordinates)

I'm convinced this is possible but I've read that an iterative method may be required and I'm not sure how to get excel to do that.

Thanks again.