Why Orbits Are Ellipses
🛰️ Orbital mechanics
Question
If the ISS is falling around the Earth, why are orbits ellipses and not perfect circles?
Newton's cannon: fire a cannonball from a high mountain. Fire it slowly and it falls to the ground; fire it faster and it lands further away; fire it fast enough and it falls around the Earth - that is orbit. A perfect circle needs exactly the right speed at exactly the right distance. Any slight difference - a bit more or less speed - and the path becomes an ellipse: the object speeds up as it falls closer to the Earth and slows down as it climbs away, trading speed for height and back again. Ellipses are the natural result of gravity plus a little bit of 'too fast' or 'too slow.'
The math
An orbit's shape is set by its total energy and angular momentum. A circle is the special case where the speed is exactly v = √(GM/r). Slightly more or less speed gives an ellipse with the Earth at one focus. The object moves fastest at perigee (closest) and slowest at apogee (farthest) - conservation of angular momentum.
Why it matters
The Moon's orbit is an ellipse (its distance varies by about 42,000 km over a month), and so are the planets' (Earth is closest to the Sun in early January, farthest in early July). 'Perfect circles' are the exception, not the rule - and the ellipse is exactly what Newton's law of gravity predicts.