Kepler Laws
Kepler Laws
Kepler’s Laws of Planetary Motion:
Johannes Kepler proposed three laws of planetary motion in 16th century. The three laws are given as below:
1. Kepler’s First Law:
It states that the path of any planet in an orbit around the sun follows the shape of an ellipse with the sun at one of its foci. The point in the orbit of a planet nearest to the sun is called perihelion and the point farthest from the sun is called aphelion.
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2. Kepler’s Second Law:
It states that an imaginary line from the sun to the planet sweeps out equal areas in equal intervals of time. Thus, if the time of travelling of a planet from P1 to P2 and from P3 to P4 is same, then the areas Area1 and Area 2 are equal.
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3. Kepler’s Third Law:
It states that the cube of the mean distance of a planet from the sun is directly proportional to the square of its orbital period T. It is expressed as
where T = time period of the planet (around the sun), r = radius as mean distance of the planet from the sun and K = Kepler constant. Kepler could not give a theory to explain the motion of planets. Newton showed that the cause of the planetary motion is the gravitational force that the sun exerts on them. Newton used Kepler’s third law to calculate the gravitational force of attraction. Suppose the orbital velocity is v and the radius of the orbit is r. Then, the force acting on an orbiting planet is given by
where, m is the mass of planet.
If ‘T’ denotes the time period, then
Substituting the value of v in Equation 1, we get
But according to Kepler’s third law of planetary motion,
Putting this value into equations, we get
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According to _________________ law given by Kepler, The path of any planet in an orbit around the sun follows the shape of an ellipse with the sun at one of its foci. | |||
| Right Option : A | |||
| View Explanation | |||
Which of the following are correct : (a) The point in the orbit of a planet nearest to the sun is called perihelion. (b) The farthest point in the orbit of a planet from the sun is called perihelion. (c) Kepler’s Second Law states that an imaginary line from the sun to the planet sweeps out equal areas in equal intervals of time. | |||
| Right Option : C | |||
| View Explanation | |||
The imaginary line from the sun to the planet sweeps ___________________________ | |||
| Right Option : B | |||
| View Explanation | |||
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