Earth's distance from sun: R

Orbital period: T

Sun's Mass: M

Earth's mass: m

Newton's Law of Universal Gravitation: F = GMm/r^2

Newton’s 2nd Law: F = ma

Okay, let's see what we can do.

Actual mass of sun: 1.989 × 10^30 kg

Error = 3.37 %

So this approximation isn't bad! The earth's orbit is not exactly a circle, though. It is an ellipse. Newton discovered that the earth and sun both orbit around a common center of mass, dispelling the idea that one orbits around the other.

Earth's distance from sun: $ R $

Orbital period: $T$

Sun's Mass: $M$

Earth's mass: $m$

Newton's Law of Universal Gravitation: $ F = \frac{GM m}{r^2} $

Newton’s 2nd Law: $ F = ma$

Okay, let's see what we can do.

Actual mass of sun: $ 1.989 * 10^{30} kg $

Error = $ 3.37 \% $

So this approximation isn't bad! The earth's orbit is not exactly a circle, though. It is an ellipse. Newton discovered that the earth and sun both orbit around a common center of mass, dispelling the idea that one orbits around the other.