WHY DOES THE ANGULAR VELOCITY INCREASES WHEN THE PLANET IS CLOE TO HE SUN.
WHY DOES THE ANGULAR VELOCITY INCREASES WHEN THE PLANET IS CLOE TO HE SUN.
By Kepler’s law of planetary motion, square of time period of revolution around the sun is proportional to the cube of radius of the orbit.
Let, T and R be the time period and radius of orbit of a planet around the sun. And, ω be the angular velocity of the planet while revolving around the sun.
Now, T2 is proportional to R3
=> T is proportional to R3/2
Thus, for planet revolving around the sun in smaller orbit will have smaller time period.
Now,
T = 2π/ω
=> ω = 2π/T
Since, angular velocity is inversely proportional to T, smaller time period will result in larger angular velocity.
Thus we conclude that planets revolving near the sun will have smaller orbital radius and smaller time period of revolution but higher angular velocity.
By Kepler’s law of planetary motion, square of time period of revolution around the sun is proportional to the cube of radius of the orbit.
Let, T and R be the time period and radius of orbit of a planet around the sun. And, ω be the angular velocity of the planet while revolving around the sun.
Now, T2 is proportional to R3
=> T is proportional to R3/2
Thus, for planet revolving around the sun in smaller orbit will have smaller time period.
Now,
T = 2π/ω
=> ω = 2π/T
Since, angular velocity is inversely proportional to T, smaller time period will result in larger angular velocity.
Thus we conclude that planets revolving near the sun will have smaller orbital radius and smaller time period of revolution but higher angular velocity.
