what are real life examples of keplers first 3 laws?

Answer 1

The first law says: "The orbit of every planet is an ellipse with the sun at one of the foci."

The second law: "A line joining a planet and the sun sweeps out equal areas during equal intervals of time."

The third law : "The squares of the orbital periods of planets are directly proportional to the cubes of the semi-major axis of the orbits."

All nine (er, eight) planets and everything else in orbit obeys all three laws. You don't have to look far for examples. They all travel in ellipses. They all sweep equal areas (which is a consequence of angular momentum conservation). Look up a couple of radii and periods in a book and confirm the third law.

Answer 2

In the 16th century, Polish astronomer Nicolaus Copernicus determined that the Earth and the planets rotate around the sun. Previously, scientists thought everything rotated around the Earth. Copernicus thought the orbits were circles.

Then about 75 years later, German mathematician Johannes Kepler found that the orbits were not circles, but ellipses. He formulated laws as to how planets and other space objects travel when in an orbit. These became known as Kepler's Laws.

Laws with examples:

The first law is that the orbit of an object moving around another in space is elliptical with the stationary object located at one of the focal points of the ellipse.

In other words, the Earth travels around the Sun in an ellipse, and the Sun is at a focal point of that ellipse. The same is true for a space satellite traveling around the Earth. It is possible for a satellite to travel in a circular orbit, but that is a special case.

Kepler's second law states that the orbiting satellite will speed up when it gets closer to the object at the focus. This is caused by the increased effect of gravity on the orbiting object as it gets closer to what it is orbiting around.

The mathematical statement of the law is that the area swept by the planet or rotating object in in giving time is the same, independent of the distance to the object at the focus. Since the areas are equal, the arc that is further away is shorter, meaning that the speed will be slower. This is not only true for objects in space but also for electrons moving around the atom.

This law shows the relationship for the time required for a planet to move around the Sun and the average distance from the Sun. The relationship is that the time squared (t2) is proportional to the distance cubed (d3). Thus, if you knew the time it took to go aournd the Sun and the distance for one planet, you could find values for another.

If t = time and d = distance for one planet, and T = time and D = distance for another planet, then:

t2 / T2 = d3 / D3

Kepler's Laws were used to explain the orbital motion of the planets around the Sun, as well as the various moons around the planets. You can use the laws to calculate the speed at any point, the time of rotation and distances for any objects in space. They can also be applied to the motion of electrons around the nucleus of an atom.

Kepler's three laws explain orbital motion. The laws are: (1) Orbits are elliptical in shape, (2) the area swept in a given time is constant for a given ellipse, and (3) the relationship for the time required for a planet to move around the Sun and the average distance from the Sun is the time squared is proportional to the distance cubed.

Dr. H