Question

What is the eccentricity of a planet's orbit if the focal distance is 8 and the major axis is 32?

Answer 1

Focal distance of an ellipse is given by the formula

$f = ae$

here a = length of semi major axis

e = eccentricity of the path

now here we know that

length of major axis for the path of planet is given as 32 units

so here we can say

$2a = 32 units$

$a = 16 units$

so length of semi major axis is 16 units

focal distance for the planet path is given as 8 units

now from the above formula we can write

$f = a*e$

$8 = 16*e$

$e = \frac{8}{16}$

$e = \frac{1}{2} = 0.5$

so eccentricity for the path of planet will be 0.5