KEPLERS LAWS OF PLANETARY MOTION
In 1543 Nicolaus Copernicus stated that all planets move SUN in circular orbits with the sun at the centre. But Johannes Kepler (1571-1630)discarded this theory and proposed the elliptical orbits for planetary motion. He formulated three laws known as Kepler laws of planetary motion.
1) KEPLER FIRST LAW(LAW OF ELLIPTICAL ORBIT )
Every Planet revolves round the sun in elliptical orbits with sun at one of the foci.
2)KEPLER SECOND LAW (LAW OF EQUAL AREAS)
The line joining the sun and plannets sweeps out equal areas in equal intervals of time. i.e, the areal velocity swept by radius vector of ellipse is a contestant.
3) KEPLER THIRD LAW (HARMONIC LAW)
The square of time period of revolution of plannet around the sin is directly proportional to cube of mean distance between sun and plannet. The proof of first law involves borh calculus and geometry... It is beyond scope of plus one and jee
EXPLANATION OF FIRST LAW
Drawing an ellipse. The string has its ends fixed at F₁ and F₂
Pencil holds the string taut
The figure shows the elliptical orbit of planet around the sun. The sun will be at one of the foci of elipse. The closest point of planet is P and it is called perihelium. The farthest point of planet is at A and it is called aphelion. Semi major axis is half of distance between perihelion and aphelion.
Proof of second law
Consider a body moving in an elliptical path as in figure. A and B are two points on elliptical patj with position co ordinates
⃗r and ⃗r+Δ r⃗ respectively
Area of ΔOAB, Δ⃗A=
(1/2)⃗rΔ⃗r
if Δt is thentime taken by planet to move from A to B then
average areal velocity
