state Kepler's third law how did it help to derive gravitational force f is directly proportional to one upon x square prove it
Answers
Answer:
Kepler's third law states that square of period of revolution (T) of a planet around the sun, is proportional to third power of average distance r between sun and planet
i.e T
2
=Kr
3
here K is constant.
If the masses of sun and planet are M and m respectively than as per Newton's law of gravitation force of attraction between them is
F=
r
2
GMm
, here G is gravitational constant The relation between G and K is described as
Explanation:
The gravitational force is providing centripetal force to the planets oribital circular motion
r
2
GMm
=
r
mv
2
⇒v=
r
GM
The time period for planet in one revolution will be T=
v
2πr
=
r
GM
2πr
squaring each side
T
2
=
GM
4π
2
r
3
comparing with given equation T
2
=Kr
3
K=
GM
4π
2
KGM=4π
2
OR
https://www.toppr.com/ask/en-in/question/keplers-third-law-states-that-square-of-period-of-revolution/
Explanation:
The Law of Ellipses
Kepler's first law - sometimes referred to as the law of ellipses - explains that planets are orbiting the sun in a path described as an ellipse. An ellipse can easily be constructed using a pencil, two tacks, a string, a sheet of paper and a piece of cardboard. Tack the sheet of paper to the cardboard using the two tacks. Then tie the string into a loop and wrap the loop around the two tacks. Take your pencil and pull the string until the pencil and two tacks make a triangle (see diagram at the right). Then begin to trace out a path with the pencil, keeping the string wrapped tightly around the tacks. The resulting shape will be an ellipse. An ellipse is a special curve in which the sum of the distances from every point on the curve to two other points is a constant. The two other points (represented here by the tack locations) are known as the foci of the ellipse. The closer together that these points are, the more closely that the ellipse resembles the shape of a circle. In fact, a circle is the special case of an ellipse in which the two foci are at the same location. Kepler's first law is rather simple - all planets orbit the sun in a path that resembles an ellipse, with the sun being located at one of the foci of that ellipse.