Kepler’s Laws

KEPLER’S LAWS

Kepler’s Laws relate to the orbits of different objects around the Earth or other planetary and celestial objects. Gravitational forces are forces between any two objects at a reasonable distance between one another. The laws are based on the idea that there aren’t any competing gravitational forces and that one object is big and one object is small (as is seen with satellites, including the moon).

Kepler has three laws. The first law is that planets around the sun have an elliptical orbit around the sun at one focus. This is seen in figure 29:

Figure 29.

Kepler’s second law states that each planet travels so that an imaginary line drown from the sun to the planet sweeps out equal areas in equal times. In other words, the planet moves fastest when it is closest to the sun.

Kepler’s third law is that the ratio of the squares of the periods of any two planets is equal to the ratio of the cubes of their average distances from the sun. The period of a planet is the time of the total path or orbit around the sun and the radius is the average (as it will differ in an ellipse over time). This means that T1 squared divided by T2 squared is equal to r1 cubed divided by r2 cubed. It means that if you know the time period of the moon (27.3 days) and the distance it is from the earth, you can calculate the period of any satellite at any distance from the earth.

Key Takeaways

• Circular motion involves an angular velocity in radians per second and a linear velocity in meters per second.

• A full circle rotation is two-pi radians in total number. Two-pi equals 360 degrees in a full circle.

• Centripetal acceleration and centripetal force are vectors that act in the direction of the center of the circle.

• Centrifugal force is a fictitious force that is felt in the opposite direction of centripetal force but is not a real force but a perceived force.

• Kepler’s laws apply to small satellites in space orbiting much larger objects in space.

• Tides are the effect of the moon and less significantly the sun on the waters surrounding the earth.