In this post, we will learn about Kepler’s three laws of planetary Motion. Johannes Kepler[1571-1630], a German astronomer and mathematician researched the location and the accurate location of the sun in the galaxy. He researched how the planets revolve around the sun and gave us the three laws. We will talk about all three laws in detail and derive the laws for their formulae.
Johannes kepler was born on 27 december 1517. He is interested in astronomy and his college professor encourages his interest. He spends most of his time researching the motion of plants. He died on 15 November 1630 in Regensburg, Germany.
First Law of Kepler – Law of Orbits
According to the first law of Kepler, All planets of our solar system move in the elliptical path and the sun is located in the focal of the elliptical path.
Second Law of Kepler – Law of Areas
According to the second law of Kepler, the imaginary line that joins the sun and the planet sweeps equal area in equal intervals of time. This law explains that the planets move slower when they are far away and move faster when they are nearer.
P1 F A1 = P2 F A2
ΔA/ΔT = L/2M
L = Angular Momentum
M = Mass of Planet
Third Law of Kepler – Law of Periods
According to the third law of Kepler, the square of the time period is directly proportional to the cube of the area.
T2 ∝ a3
The shorter the orbit of the planet around the sun, the shorter the time taken to complete one revolution. Using the equations of Newton’s law of gravitation and laws of motion, Kepler’s third law takes a more general form.
P2 = 4π2 /[G(M1+ M2)] × a3