Newton’s Laws, Orbital Revolutions, & Heliocentric Solar System
With his laws of motion and gravity Newton resolved the heliocentric vs. geocentric controversy and explained what causes orbits.
Geocentric Vs. Heliocentric
Building on the work of other ancient Greeks, Ptolemy proposed a geocentric model of the cosmos. He thought Earth was at the center of the cosmos, and the Sun, Moon, planets, and stars revolved around Earth.
In the 16th century, Copernicus proposed a heliocentric model of the solar system. He suggested that Earth and other planets revolve around the Sun. The controversy raged; was the cosmos geocentric or heliocentric? Copernicus unfortunately did not suggest a physical reason why the planets should orbit the Sun.
Newton’s Laws Require Planets to Orbit Sun
Newton’s first law says an object can change the speed or direction of its motion, that is accelerate, only if an external force acts on it. According to his second law, more massive objects require more force to accelerate. Newton’s third law requires that the gravitational force the Sun exerts on the Earth be equal to, but in the opposite direction as, the gravitational force the Earth exerts on the Sun.
The force the Earth exerts on the Sun is equal in magnitude to the force the Sun exerts on the Earth, however the Sun is very much more massive than Earth. So, this force will affect Earth much more than the Sun. Earth, and other planets, therefore orbit the Sun, which remains nearly stationary. Mutual gravitational forces accelerate the less massive object more. It is the same reason why we fall down towards the Earth, and the Earth does not fall up towards us.
How Gravity Causes Orbits
Tie a weight onto the end of the string, Twirl it around in a circle. Notice that the force of the string acting on the weight, called its tension, acts towards the center of the circle. Any force towards the center of a circular motion is a centripetal force. Also notice that if you let go of the string, the weight flies off in a straight line.
An object only accelerates when an external force acts on it. If the force is perpendicular to the direction of velocity, the acceleration changes the direction of velocity rather than the speed.
Just as for the weight on a string, the gravitational force the Sun exerts on a planet is perpendicular to the direction of the planet’s velocity. Gravity supplies the centripetal force that planets need to orbit the Sun. Acting like a string, the Sun’s gravitational force constantly changes the direction of the planet’s velocity so that it revolves in a nearly circular orbit around the Sun. Earth’s gravity causes the Moon to orbit the Earth the same way.
Were gravity to suddenly disappear, Earth and the other planets would continue to move in a straight line according to Newton’s first law.
Center of Mass
Earth and planets orbit the Sun because they are much less massive than the Sun. If two objects, say two stars, have the same mass, then they each orbit a point half way between them, the mutual center of mass.
We say that planets orbit the Sun, but technically they each orbit the mutual center of mass. Because the Sun is so much more massive than the planets, the mutual center of mass is very close to, but not exactly at, the center of the Sun. Planets revolve in a very large orbit around the Sun. The Sun’s very small orbit around the mutual center of mass produces an extremely small wobble.
This barely detectable wobble in other stars allows us to detect extrasolar planets.
Newton’s laws resolved the geocentric vs. heliocentric controversy and tell us why planets orbit the Sun.