Kepler’s Laws
We will cover following topics
Kepler’s Laws
Kepler’s Three Laws: Kepler’s three laws are stated below:
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The orbit of a planet is an ellipse with the Sun at one of the two foci.
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A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time.
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The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit.
PYQs
1) Prove that the path of a planet, which is moving so that its acceleration is always directed to a fixed point (star) and is equal to \(\dfrac{\mu}{(distance)^2}\) is a conic section. Find the conditions under which the path becomes
(i) ellipse,
(ii) parabola and
(iii) hyperbola
[2019, 15M]
2) The force of attraction of a particle by the earth is inversely proportional to the square of its distance from the earth’s centre. A particle, whose weight on the surface of the earth is \(W\), falls to the surface of the earth from a height \(3h\) above it. Show that the magnitude of work done by the earth’s attraction force is \(\dfrac{3}{4}hW\), where \(h\) is the radius of the earth.
[2019, 10M]
3) A comet describing a parabola under inverse square law about the sun, when nearest to it suddenly breaks up, without gain or loss of kinetic energy, into two equal portions, one of which describes a circle. Prove that the other will describe a hyperbola of eccentricity 2.
[2001, 15M]