Kepler’s 3 Laws of planetary motion

Johannes Kepler 1571-1631: Assistant to astronomer Tyco Brahe Developed the three laws of planetary motion still used today. Every planet orbits in an ellipse around the sun. Every planet sweeps out an equal amount of area in an equal amount of time during it’s orbit. Close planets orbit the sun faster than farther planets.

Kepler’s Laws Explain the ways in which planetary bodies move around their suns. Kepler did not understand how the force of gravity influenced the motions of these planets. His laws of planetary motion were developed based solely upon his analysis of Tyco Brahe’s observations, his own observations and an earlier system of planetary motion rules developed by Copernicus. These laws are still accepted today as the rules for the motion of planets; newer scientists, (Newton), have expanded upon these laws and explained them in terms of gravity, but the general rules are the same.

Kepler’s 1st Law “The orbit of a planet is an ellipse with the Sun at one of the two foci.” This law states that each planet revolves around the sun in an elliptical shape, with the star it revolves around NOT at the center of the ellipse, but at one of its focal points.

Kepler’s 2nd Law “A line segment joining a planet and the sun sweeps out equal areas during equal intervals of time.” This law states that as a planet revolves around its sun, an imaginary straight line connecting the sun and the planet will move so that an equal area is covered in an equal length of time as the planet revolves. See the graphics that follow:

Kepler’s 3rd Law “The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.” This law explains that the length of a planet’s year, (how long it takes the planet to orbit the Sun), is proportional to how far away from the sun that planet is. In other words, planets that are closer to the sun will complete their orbits faster than those that are farther away from the sun, even if the planets that are farther away are moving faster……they still have farther to travel!!

Kepler’s 3rd Law The mathematical formula for Kepler’s 3rd Law is P2/D3. P = the length of the planet’s year, (how long it takes for the planet to revolve around the sun). D = the average distance from the planet to the sun. This law essentially says that the ratio of the length of a planet’s year to it’s distance from the sun is the same for every planet. For every planet in the solar system, if you put the length of it’s year into the ‘P’ in the above equation, and it’s average distance from the sun in the ‘D’, you will get the same number for all 8 planets. What is implied by this is that the farther away a planet is from the sun, the longer it’s year will be. But it will always revolve around the sun in a fixed amount of time, determined by how far away from the sun it is.

Sir Isaac Newton Newton is famously known for creating his 3 laws of motion, as well as for inventing the mathematical field of calculus in order to solve his own problems. Newton’s 3 laws of motion: Inertia, (objects at rest stay at rest, objects in motion stay in motion). Force equals mass times acceleration, (F = MA) Action – Reaction

Sir Isaac Newton However, it was by studying Kepler’s 3rd law of planetary motion that Newton was able to develop his own law for the force of gravity that exists between ANY two objects, celestial or otherwise: Because this equation shows the force of gravity that exists between any 2 objects, it is referred to as the universal law of gravitation.

Universal Law of Gravitation Newtons equation can be used to calculate the amount of gravitational force between any two celestial objects, such as: Between a planet and it’s sun Between 2 planets Between a planet and it’s moon But we now know that ALL objects, (anything that has mass), exerts a force of gravitation on all other objects around it, no matter how small that force may be. ….so right now, YOU are exerting a force of gravity on the person sitting next to you! But because you’re mass is so small, (relatively speaking), you do not notice this incredibly small force. Much larger objects such as planets exert a much larger force of gravity on other objects, such as the Earth pulling down on you, (which is why you always fall towards the Earth!)

Which has more gravitational pull? Let’s use Newton’s Universal Law of Gravitation to find out: Who has a greater gravitational pull on you right now? Mr. Firman? Or… The Moon?