1) The orbit of a planet is an ellipse with the sun at one of the foci.
2) The line drawn between a planet and the sun sweep out equal areas in equal times.
3) The square of the periods of the planets is proportional to the cubes of their mean distance from the sun.
So what is that telling us? In a nutshell, all orbits are ellipses, the close to the body you are orbiting the faster you go (e.g. if you have a highly elliptical orbit the satellite or planet’s velocity will increase as it approaches the object being orbited and decrease as it get further away).
These laws not only apply to planets and satellites, but to any orbiting body.
Note: Geek alert #1:
For an orbiting body this is not entirely correct. It turns out that both bodies end up orbiting a common center of mass of the two-body system. However, for satellites, the mass of the Earth is so much greater than the mass of the satellite, the effective center of mass is the center of the Earth.
Newton’s three laws (and law of gravitation):
1) The first law states that every object will remain at rest or in uniform motion in a straight line unless compelled to change its state by the action of an external force. (Commonly known as inertia)
2) The second law states that force is equal to the change in momentum (MV) per change in time. (For a constant mass, force equals mass times acceleration F=ma)
3) The third law states that for every action there is an equal and opposite reaction. In other words, if an object exerts a force on another object, a resulting equal force is exerted back on the original object.
Newton’s law of gravitation states that any two bodies attract one another with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
Note: Geek alert #2:
Actual observed positions did not quite match the predictions under classical Newtonian physics. Albert Einstein later solved this discrepancy with his “General Theory of Relativity”. There are four classical “tests” that cemented General Relativity:
1. In November of 1919, using a solar eclipse, experimental verification of his theory was performed by measuring the apparent change in a stars position due to the bending of the light buy the sun’s gravity.
2. The changing orientation of the major axis or Mercury not exactly matching classical mechanics.
3. Gravitational Redshift
4. Gravitational Time Dilation
Applause!
:-)