Keplar’s law and Kepler’s motion by Rushabh.pptx

Keplar’s law and Kepler’s motion by Rushabh.pptx

1. Keplar’s law and Kepler’s motion Submitted by Rishabh kumar , Department of Geography, Panjab university

2. Introduction Kepler gave three laws about the motions of planets at that time when there was the authority of church and no one was to believe him. People believed that plants rotate around the sun in the circular path and not in elliptical orbit Also the speed of the planets is not same everywhere in the path followed. Planets are not at the same distance from sun while orbiting it. It is also believed that keplar stole these laws from Tycho Brahe but there is no authenticity of this statement.

3. Keplar laws of planetary motion All planets revolve around the sun in closed elliptical orbits and sun is at one focus of ellipse. Planets do not revolve around sun with constant speed – Planets move faster when it is near to sun and slower when it is farther from sun. Hence, the areal velocity of a planet is constant. i.e. A planet sweeps equal area in equal time around sun. The cube of mean distance of a planet from the sun is proportional to the square of its orbital period T

4. What is ellipse a. Distance ‘a’ Distance ‘a’ Distance ‘2a’ (major axis of ellipse) Distance ‘b’ Distance ‘b’ These two are monor axis

5. F1 F2 Ellipse has two focus The equation of ellipse is Where ‘e’ is eccentricity, It tells how ellipse is snug. How much it is deviated from circle. If ‘e’ is zero, it will become circle. It’s value lies between 0 and 1 Distance ‘ae Distance ‘ae’ ae,0 -ae,0 a,0 -a,0 0,-b 0,b Law 1 st = All planets revolve around the sun in closed elliptical orbits and sun is at one focus of ellipse.

6. Explanation of first law Planets will not be at equal distance from sun. When planet is the closest to the sun it is called Periphelion The closest distance between planet and sun is r = a – ae or r = a(1-e) When the planet is farthest from the sun it will be called Apihillion or Aphogee and distance will be r = a+ae or r = a(1+e) Closest planet Farthest planet

7. Explanation of 2 nd Law Planets do not revolve around sun at constant speed. Planets move faster when it is near to sun and slower when it is farther from sun. The areal velocity of the planet is constant. (Actual Law). A planet sweeps equal area in equal time around the sun. Suppose planet swept area from A to B in one second. It will sweep Equal area everywhere in the path. If area swept equal then path will be reduced A B

8. What is areal velocity ? dA / dt is constant i.e change is area upon change in time will be constant.

9. Keplar 3 rd law Planet p1 revolves whole around the sun in T1 time and p2 at T2 time then (T2/T1) 2 = (r2/r1) 3 . While the exact law is T 2 ∞ a 3 .as it is elliptical path and not a circle. r1 r2 p1 p2

10. Thank you