# Kepler´s laws of planetary motion

### Kepler´s laws of planetary motion

The three important laws describing planetary motion were formulated by Johannes Kepler.

Physics

Keywords

Kepler, planetary motion, focal point, ellipse, radius vector, orbital period, planet, Solar System, gravity, circulatory system, mechanics, astronomy, astronomer, physics

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### Kepler´s 1st law

• minor axis
• major axis
• focal point 1 - It is true for all points of the elliptical orbit that the sum of their distances from two focal points is constant.
• focal point 2 - It is true for all points of the elliptical orbit that the sum of their distances from two focal points is constant.

According to Kepler´s first law of planetary motion, the orbit of each planet is an ellipse with the Sun at one of its foci.

Kepler published his first law in 1609, breaking with the more than 2000-year-old belief that orbits were perfect circles. This doctrine caused serious problems in both the geocentric Ptolemaic system and the heliocentric model put forward by Copernicus: these models assumed a complex interaction of circles in their description of the motion of celestial objects. By abandoning the idea of circular orbits in favour of elliptical orbits, the description of planetary motion was simplified.

### Kepler´s 2nd law

• A₁ - The area swept by the line joining a planet and the Sun (the radius vector) per given time units.
• A₂ - The area swept by the line joining a planet and the Sun (the radius vector) per given time units.
• focal point 1 - It is true for all points of the elliptical orbit that the sum of their distances from two focal points is constant.
• focal point 2 - It is true for all points of the elliptical orbit that the sum of their distances from two focal points is constant.

According to Kepler´s 2nd law, the line joining a planet and the Sun (the radius vector) covers equal areas during equal intervals of time. That is, at the perihelion, when the planet is near the Sun and thus the radius vector of its orbit is shorter it moves faster than at the aphelion.

The speed of the Earth at the perihelion is 30.29 km/s, while at the aphelion it is 29.29 km/s. The orbit of Mercury is more eccentric, therefore its orbital speed is 58.98 km/s at the perihelion and 38.86 km/s at the aphelion.

### Kepler´s 3rd law

• major axis (a₁) - For the sake of simplicity we have chosen elliptical orbits whose major axes are on the same line. In the Solar System this is not true for the planetary orbits but this does not change the validity of Kepler´s 3rd law.
• major axis (a₂)

According to Kepler´s 3rd law, the square of the orbital period of a planet is directly proportional to the cube of the major axis of its orbit. This means that the orbital period of planets further from the Sun is longer.

Mercury, which is the nearest planet to the Sun, has an orbital period of about 88 Earth days, the Earth´s orbital period is 365 days, while that of Neptune, the outermost planet in the Solar System, is more than 160 Earth years.

In the formulation of Kepler´s 3rd law, semi-major axes are often used instead of major axes, but this does not change the validity of the law.

Kepler´s laws, which were based on data from Tycho Brache´s astronomical observations, represented the foundation of celestial mechanics. The three laws also provided a basis for Isaac Newton´s theory of gravity, explaining the physics of planetary motion.

### Solar System

• Sun
• Mercury - Average distance from the Sun: 57 909 176 km Orbital eccentricity: 0.206 Orbital period: 87.97 days
• Venus - Average distance from the Sun: 108,200,000 km Orbital eccentricity: 0.0068 Orbital period: 224.7 days
• Earth - Average distance from the Sun: 149,600,000 km Orbital eccentricity: 0.0167 Orbital period: 365.25 days
• Mars - Average distance from the Sun: 227,936,637 km Orbital eccentricity: 0.093412 Orbital period: 1.88 years
• Jupiter - Average distance from the Sun: 778,300,000 km Orbital eccentricity: 0.048 Orbital period: 11.86 years
• Saturn - Average distance from the Sun: 1 426,725,413 km Orbital eccentricity: 0.054 Orbital period: 29.46 years
• Uranus - Average distance from the Sun: 2,871,000,000 km Orbital eccentricity: 0.047 Orbital period: 84.01 years
• Neptune - Average distance from the Sun: 4,504,300,000 km Orbital eccentricity: 0.0086 Orbital period: 164.79 years

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