Haileys comet has an elliptical orbit with the sun at one fo

Hailey\'s comet has an elliptical orbit with the sun at one focus. The eccentricity of the orbit is approximately 0.97. The length of the major axis of the orbit is approximately 35.88 astronomical units. (An astronomical unit is about 93 million miles.) Find the standard form of the equation of the orbit. Place the center of the orbit at the original and place the major axis on the x-axis.

Solution

major axis , 2a = 93 mill miles

eccentricity :e =0.97

a = 46.5

b = a*sqrt(1 -e^2) = 46.5sqrt( 1- 0.97^2) = 11.30

x^2/a^2 + y^2/b^2 = 1

So,