How to find Kepler's law from Newton's laws

In summary, the conversation discussed an experiment where the equation T2=(4π2m)/Mgr was used to prove the relationship between time, mass, and radius of rotation. The experiment also related this equation to Newton's laws by using the equations F=Mgm/r2 and F=mv2/r. It was then mentioned that there is a difference between "g" and "G", with g representing the acceleration of gravity and G representing the Gravitational Constant. The speaker also asked for clarification on how to reach the original formula using Newton's laws.
  • #1
Grimlock_smash
1
0
We were asked to do an experiment where we had to prove the equation:
T2=(4π2m)/Mgr
Where M is the mass of the mass stack in kg (0.3kg), m is the mass of the rubber bung in kg (0.0226kg), T is the time taken for one rotation in seconds, r is the horizontal radius of rotation in meters, and g is the strength of gravity (9.8Nkg-1).

And I tried to relate this to Newton's laws in my report by using:
F=Mgm/r2
and F=mv2/r

Which gave me:
T2=(4π2r3)/Mg

How do I reach the original formula using Newton's laws?
 
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  • #2
:welcome:
Make sure you know there is a difference between "g" and "G".
g is the acceleration of gravity (about 9.8 m/s2)
G is the Gravitational Constant (6.67 × 10-11 m3/kg⋅s2)
 

1. How do Kepler's laws relate to Newton's laws?

Kepler's laws of planetary motion were derived from Newton's laws of motion and universal gravitation. In other words, Kepler's laws are a consequence of Newton's laws and explain the behavior of objects in orbit around a central body, such as planets orbiting the sun.

2. What is the first law of Kepler?

The first law, also known as the law of ellipses, states that all planets move in elliptical orbits with the sun at one focus. This means that the distance between a planet and the sun varies throughout its orbit, with the closest point being the perihelion and the farthest point being the aphelion.

3. How does Newton's law of gravitation explain the second law of Kepler?

The second law, also known as the law of equal areas, states that a line connecting a planet to the sun sweeps out equal areas in equal times. This is explained by the fact that as a planet moves closer to the sun, it experiences a stronger gravitational force, causing it to accelerate and cover a larger distance in a shorter amount of time.

4. What is the relation between the third law of Kepler and Newton's law of universal gravitation?

The third law, also known as the law of harmonies, states that the square of a planet's orbital period is proportional to the cube of its semi-major axis. This can be derived from Newton's law of universal gravitation, as the strength of the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

5. Can Kepler's laws be applied to objects other than planets?

Yes, Kepler's laws can be applied to any two objects in orbit around each other, such as moons orbiting a planet or artificial satellites orbiting the Earth. As long as the objects are following an elliptical path and are subject to a gravitational force, Kepler's laws can be used to describe their motion.

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