"Kepler discovered that the path of Earth around the sun is an ellipse with the sun at one of the foci. let r(t) be the position vector from the center of the sun to the center of the Earth at time t. Let w be the vector from Earth's South Pole to North Pole. It is known that w is constant and not orthogonal to the plane of the ellipse (Earth's axis is tilted). In terms of r(t) and w, give the mathematical meaning of (i)perihelion, (ii) aphelion, (iii) equinox, (iv) summer solstice, (v) winter solstice." Copied from ISBN 032119800X.
I am not sure where to start. What I am really trying to do with this problem is find out at what degree from the perihelion to where we would be at a specific date, and such. Along with that, what path the sun would take in the sky given a coordinate on earth, as well as the path of the moon. I know that it's a way complicated problem, but I have nowhere else to go.
I have tried things like using Kepler's Second Law and polynomial series, using the polar area formula and the polar form of Earth's orbit to find the time it would take to get from one place to another, but testing my results always came out messed up. That also doesn't answer my question of what kind of sunlight I get at 61.11N 149.50W.
Hope you enjoy the challenge, I've spent a couple of months trying to figure all of this out. Danke!
-Josh
I am not sure where to start. What I am really trying to do with this problem is find out at what degree from the perihelion to where we would be at a specific date, and such. Along with that, what path the sun would take in the sky given a coordinate on earth, as well as the path of the moon. I know that it's a way complicated problem, but I have nowhere else to go.
I have tried things like using Kepler's Second Law and polynomial series, using the polar area formula and the polar form of Earth's orbit to find the time it would take to get from one place to another, but testing my results always came out messed up. That also doesn't answer my question of what kind of sunlight I get at 61.11N 149.50W.
Hope you enjoy the challenge, I've spent a couple of months trying to figure all of this out. Danke!
-Josh