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Kepler`s Laws

German astronomer Johann Kepler empirically discovered the three laws of planetary motion in the beginning of XVII century. Kepler's discoveries were based on the long-term observations made by the Danish astronomer Tiho Brahe.

First Kepler's law states that that the orbits of planets are ellipses, with the Sun at one focus. A modern formulation of the first law states that an orbit of a moving body in undisturbed motion is a second-order curve - ellipse, parabola or hyperbola.

Second Kepler's law (also known as the law of equal areas) states that the planet's radius vector circumscribes equal areas during equal periods of time. In other words, the angular momentum is conserved, and the angular speed of a planet is always constant.

Third Kepler's law states that the square of the orbits is proportional to the cube of their large semi-major axis, and that the constant of proportionality is independent of the individual planets.

Unlike the first and second laws, Kepler's third law is applicable to elliptical orbits only.

This model illustrates a satellite moving along its orbit with the Earth at the orbit's center. Modify the orbital parameters (distance to the Earth's in perigee and initial velocity) by using input windows in the lower part of the model.

A separate message window displays other orbital parameters, such as the length of the large and small semi-axes, eccentricity and rotation period, as well as the elapsed time since the initiation of the experiment.

Press "Run" button to activate the model. "Stop" and "Reset" buttons suspend and return the model to its initial state, respectively. Use appropriate buttons to select one of the three Kepler's laws to observe.

You may turn an elliptic orbit into a hyperbolic one by changing the initial velocity of the celestial body. Certain comets and some satellites leaving the Solar system move along hyperbolic orbits in respect to the Sun.

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