Question to Find Maximum Distance in the Elliptical Orbit

Topic : Ellipse

Question : Halley's comet has an elliptical orbit with the sun at one focus and a major axis of 1,636,484,848 miles. The closest the comet comes to the sun is 54,004,000miles. What is the maximum distance from the comet to the sun?

Solution :

2a = 1,636,484,848miles
so SC = 54,004,000miles
maximum distance from comet to the sun will be DS.
That is when comet comes at D
there is a maximum distance from sun
So SD = CD - SC ; CD = major axis = 1,636,484,848 miles
= 1,636,484,848 - 54004000
= 1582480848miles
So maximum distance is 1582480848miles.