state kepler's laws of plantery motion and explain how newton guessed inverse square rule
Answers
Answer:
Kepler's first law :
The orbit of a planet is an ellipse
with the Sun at one of the foci.
Kepler’s second law :
The line joining the planet and the
Sun sweeps equal areas in equal intervals
of time.
AB and CD are distances covered by
the planet in equal time i.e. after equal in- tervals of time, the positions of the planet
starting from A and C are shown by B and
D respectively.
Kepler’s third law :
The square of its period of revolution around the Sun is directly proportional to
the cube of the mean distance of a planet from the Sun.
Thus, if r is the average distance of the planet from the Sun and T is its period of
revolution then,
T2
a r3 i.e.
Kepler’s first law :
A
C
F1 F2
Kepler obtained these laws simply from the study of the positions of planets obtained
by regular observations. He had no explanation as to why planets obey these laws. We
will see below how these laws helped Newt
Newton's inverse square law states that gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The Newton's inverse square law is deduced from Kepler's 'Third law' of planetary motion. Kepler saw that planets move around in an elliptical orbit.
Centripetal force on planet is calculated as :
F =
r
mv
2
=
r
m
(
T
2πR
)
2
=
rT
2
4π
2
mr
2
F =
r
2
4π
2
m
T
2
r
3
But from Kepler's law,
T
2
r
3
is constant for planets
Therefore F =
r
2
4π
2
m
i.e K =
r
2
G
From this the square inverse nature of gravitational force was derived by Newton.
Answer:
Newton's inverse square law states that gravitational attraction force between two point masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The Newton's inverse square law is deduced from Kepler's 'Third law' of planetary motion. Kepler saw that planets move around in an elliptical orbit.
Centripetal force on planet is calculated as :
Explanation:
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