Kepler's Laws of Planetary Motion
The German scientist Johannes Kepler published 3 laws describing planetary motion around the sun :
1) The Law of Equal Areas - An imaginary line connecting the centre of the sun to the centre of a planet will sweep out equal areas in equal intervals of time. This law describes the speed at which planets move while orbiting the sun. A planet's speed is at it's maximum when at it's perihelion (closest to the sun) and minimum when at it's aphelion (furthest from the sun).
This can be illustrated in the aforementioned diagram, which shows the relationship between the sun and the earth. The magnitude of the area of the triangles above is constant.
1) The Law of Equal Areas - An imaginary line connecting the centre of the sun to the centre of a planet will sweep out equal areas in equal intervals of time. This law describes the speed at which planets move while orbiting the sun. A planet's speed is at it's maximum when at it's perihelion (closest to the sun) and minimum when at it's aphelion (furthest from the sun).
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| The first law |
For example, the wide but short triangle on the left will have the same areas as the one opposite to it, and so on.
2) The Law of Ellipses - Orbits of planets around the sun are elliptical in shape, and the centre of the sun located at one focus. This law isn't quite as difficult to understand as the others, but is still important. The orbit of the earth around the sun is shown below :
Orbital eccentricity is a value that describes by how much an object's orbit deviates from a perfect circle, with 0 being a circle and 1 being completely elliptical. Earth has an eccentricity of 0.0167086, making it quite close to a circle but more elliptical.
3) The Law of Harmonies - This law describes the radius as well as orbital period (the time it takes to complete one orbit around the sun) of different planets in the solar system. The comparison being made is that the ratio of the period squared to the average distance from the sun cubed is the same for every single planet. T^2/R^3 (period squared divided by radius cubed) can be calculated using :
2) The Law of Ellipses - Orbits of planets around the sun are elliptical in shape, and the centre of the sun located at one focus. This law isn't quite as difficult to understand as the others, but is still important. The orbit of the earth around the sun is shown below :
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| Orbit of the earth relative to the sun |
3) The Law of Harmonies - This law describes the radius as well as orbital period (the time it takes to complete one orbit around the sun) of different planets in the solar system. The comparison being made is that the ratio of the period squared to the average distance from the sun cubed is the same for every single planet. T^2/R^3 (period squared divided by radius cubed) can be calculated using :
Where P represents the time taken for the planet to complete one orbit in seconds and a is the average distance between the planet and the sun in metres. To prove this, the ratio for earth can be calculated by plugging in :
The value turns out to be approximately 2.977 * 10^-19 (s^2/m^3).
The same can be done for, say, Venus :
The value thus turns out to be approximately 2.989*10^-19 (s^2/m^3). Evidently, this value is quite close to that of earth's and therefore Kepler's third law of planetary motion is verified.
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