Question

A comet has a period of 100 years. The distance of closest approach is .5 AU. Calculate the eccentricity?

Answer 1

note that the focus is at distance of (ae) from the origin, where a=21.54 do you need further help.

Answer 2

Could explicate more? thanks

Answer 3

since the sun is always at the focus, and the trajectory of the comet is always an ellipse, the distance of the sun from the center of the ellipse is ae, where ais the major axis (the Rav) and e is the eccentricity.
from the diagram, distance of sun =a-5=ae.
since a=21.54 (your calc) ,find e.

Answer 4

I go .977

Answer 5

yup! :) you've got it.