In Newton’s view of the universe, space is unchanging and Euclidean. In
Euclidean, or “flat”, space, all the axioms and theorems of plane geometry
(as codified by Euclid in the third century BC) hold true. In Euclidean space,
the shortest distance between two points is a straight line, the angles at the
vertices of a triangle sum to π radians, the circumference of a circle is 2π times
its radius, and so on, through all the other axioms and theorems you learned
in high school geometry. In Newton’s view, moreover, an object with no net
force acting on it moves in a straight line at constant speed. However, when
we look at objects in the Solar System such as planets, moons, comets, and
asteroids, we find that they move on curved lines, with constantly changing
speed. Why is this? Newton would tell us, “Their velocities are changing
because there is a force acting on them; the force called gravity.”