LearnMechanics & orbitsNaked eye
Eccentricity
How far an orbit departs from a circle, from 0 for a perfect circle to just under 1 for a very elongated ellipse.
Why it matters
It decides how much a planet's distance — and therefore its brightness and apparent size — changes through its year. Mars at 0.093 is the reason some oppositions are far better than others.
The maths, in layers
1 · Intuition
Eccentricity is the offset of the focus from the centre, measured in units of the semi-major axis.
2 · The equation
e = c / a = (r_max − r_min) / (r_max + r_min)
- c
- distance from centre to focus
- a
- semi-major axis
- r_max, r_min
- aphelion and perihelion distances
In practice
A perihelic Mars opposition shows a disc about 25 arcseconds across; an aphelic one barely 14. Same planet, same telescope, entirely different night.
Rests on
Nothing. This is a starting point — you can begin here.