Question
Given that:
- Time taken for Mercury to orbit Sun = 88 days
- Eccentricity of Mercury's orbit around the Sun = 0.206
- Average distance between Mercury and Sun = 0.387 AU
- 1 Astronomical Unit (AU) = 149, 597, 870, 700 metres
Develop a model, using parametric equations, to show the path of Mercury around the Sun.
My thinking
I've thought about Kepler's first law and how the sum of the distances from a point to both foci (one being the sun) is equal to the major axis of the ellipse. I guess this could be useful because I have the average distance between mercury and the sun, but I'm not sure how to work out the distance from the other focus to the point where mercury is at. Every other method I though of requires already knowing the length of one of the axis, so no good.
There was a tip at the end of the question saying the "average value of a function equation" could be useful- I've attached it, but I'm yet to find a use for it in the problem.
This problem's been racking my brain for a while now, hope to get some much needed help
Given that:
- Time taken for Mercury to orbit Sun = 88 days
- Eccentricity of Mercury's orbit around the Sun = 0.206
- Average distance between Mercury and Sun = 0.387 AU
- 1 Astronomical Unit (AU) = 149, 597, 870, 700 metres
Develop a model, using parametric equations, to show the path of Mercury around the Sun.
My thinking
I've thought about Kepler's first law and how the sum of the distances from a point to both foci (one being the sun) is equal to the major axis of the ellipse. I guess this could be useful because I have the average distance between mercury and the sun, but I'm not sure how to work out the distance from the other focus to the point where mercury is at. Every other method I though of requires already knowing the length of one of the axis, so no good.
There was a tip at the end of the question saying the "average value of a function equation" could be useful- I've attached it, but I'm yet to find a use for it in the problem.
This problem's been racking my brain for a while now, hope to get some much needed help