# Thread: [SOLVED] An ugly PP calc word problem

1. ## [SOLVED] An ugly PP calc word problem

I found this on a power point on the net and trying to solve it.
Its a conic section from the ellipse chapter.

• The mean distance of Mars from the Sun is 142 million miles.
• Perihelion = 128.5 million miles
• 1. What is Aphelion = ??
• 2. Equation for Mars orbit?
• Round to nearest tenth if necessary.
• Hint: Orbit of a planet about the sun is an Ellipse, with the Sun at one focus. Aphelion of a planet is its greatest distance from the Sun and the perihelion is its shortest distance. Mean distance of a planet from the sun is the length of the semi major axis of the elliptical orbit.

1. Aphelion
2. Equation

2. The equation of an ellipse, whose center is at (0,0):
[(x^2)/(a^2)] +[(y^2)/(b^2)] = 1 ------------(i)
Also,
b^2 = a^2 -c^2 -----------------------------(ii)
where
a = semi-major axis ----mean distance in this Problem.
b = semi-minor axis
c = focal distance, from the center
(x,y) is any point on the ellipse.

So,
perihelion +aphelion = 2a = 2(mean distance)
128.5 +aphelion = 2(142)
aphelion = 284 -128.5 = 155.5 million miles -------answer.

-----------------------------
Equation of Mars' orbit:

c = "a" minus perihelion = mean distance minus perihelion ----(1)
c = 142 -128.5 = 13.5 million miles

Hence,
b^2 = (142)^2 -(13.5)^2
b^2 = 19,981.75 --------------------------(***)

Therefore, the equation of Mars' orbit is
[(x^2)/(142^2)] +[(y^2)/(19,981.75)] = 1