There is a common misconception that the Copernican model did away with the need for epicycles. As a consequence, the Copernican model, with its assumption of uniform circular motion, still could not explain all the details of planetary motion on the celestial sphere without epicycles.

There were seven planets, or wandering stars, because they had a course through the zodiac in addition to traveling around the earth: the moon, Mercury, Venus, the sun, Mars, Jupiter. Beyond that were the fixed stars.

In 1514, Copernicus distributed a handwritten book to his friends that set out his view of the universe. In it, Copernicus established that the planets orbited the sun rather than the Earth. He laid out his model of the solar system and the path of the planets.

Tycho Brahe

The fact that planets travel on elliptical paths is known as Kepler’s First Law. Once he understood that planets traveled in ellipses, he determined that an invisible line connecting the sun to a planet covered an equal amount of area over the same amount of time.

There are actually three, Kepler’s laws that is, of planetary motion: 1) every planet’s orbit is an ellipse with the Sun at a focus; 2) a line joining the Sun and a planet sweeps out equal areas in equal times; and 3) the square of a planet’s orbital period is proportional to the cube of the semi-major axis of its …

Kepler’s First Law: each planet’s orbit about the Sun is an ellipse. The Sun’s center is always located at one focus of the orbital ellipse. The Sun is at one focus. The planet follows the ellipse in its orbit, meaning that the planet to Sun distance is constantly changing as the planet goes around its orbit.

“The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit” That’s Kepler’s third law. In other words, if you square the ‘year’ of each planet, and divide it by the cube of its distance to the Sun, you get the same number, for all planets.

Thus Kepler’s 3rd Law is approximately valid because the Sun is much more massive than any of the planets and therefore Newton’s correction is small. However, detailed observations made after Kepler show that Newton’s modified form of Kepler’s 3rd Law is in better accord with the data than Kepler’s original form.

Newton developed a more general form of what was called Kepler’s Third Law that could apply to any two objects orbiting a common center of mass. This is called Newton’s Version of Kepler’s Third Law: M1 + M2 = A3 / P2. Special units must be used to make this equation work.

Orbital Speed determines the orbit shape: Circular Speed. Escape Speed.

There is a simplified version of this law: P2 = a3 where: The object must be orbiting the Sun. P = period of the orbit in years. a = average distance of the object from the Sun in AU.

Kepler’s third law, which is often called the harmonic law, is a mathematical relationship between the time it takes the planet to orbit the Sun and the distance between the planet and the Sun. The time it takes for a planet to orbit the Sun is its orbital period, which is often simply called its period.

Kepler’s third law (the Harmonic Law), relates the orbital period of a planet (that is, the time it takes a planet to complete one orbit) to its mean distance from the Sun. This law states that the closest planets travel at the greatest speeds and have the shortest orbital periods.

Kepler’s Laws are wonderful as a description of the motions of the planets. Moreover, Kepler’s Third Law only works for planets around the Sun and does not apply to the Moon’s orbit around the Earth or the moons of Jupiter.

Perihelion

The reason orbits are not circular is illustrated by Newton’s universal law of gravity, which postulates that the force of gravity weakens as the square of the distance between the two objects; the two objects being the planet and star or planet and natural satellite.

Kepler’s first law implies that the Moon’s orbit is an ellipse with the Earth at one focus. The distance from from the Earth to the Moon varies by about 13% as the Moon travels in its orbit around us. A straight line drawn from the planet to the Sun sweeps out equal areas in equal times. …

These laws can be applied to model natural objects like planets, stars, or comets, as well as man-made devices like rockets and satellites in orbit. Although Kepler originally developed his laws in the context of planetary orbits, the results hold for any system with a radial force obeying the inverse square law.

Except for Mercury, the planets in the Solar System have very small eccentricities. That is believed to be due to tidal circularization, an effect in which the gravitational interaction between two bodies gradually reduces their orbital eccentricity. …

Although some objects follow circular orbits, most orbits are shaped more like “stretched out” circles or ovals. If the eccentricity is close to zero, the ellipse is more like a circle. Earth moves around the Sun in an elliptical orbit. Earth’s orbit is almost a perfect circle; its eccentricity is only 0.0167!

If Earth’s orbit was a perfect circle, the Sun would cross the meridian at noon every day (ignoring daylight savings time). But our orbit is slightly oval-shaped. In July, we are at our furthest point from the Sun, and Earth moves slower than average along its path.

If Earth had two moons, it would be catastrophic. An extra moon would lead to larger tides and wipe out major cities like New York and Singapore. The extra pull of the moons would also slow down the Earth’s rotation, causing the day to get longer.