Newtons theory of gravity : satelite orbits and ellipses

In summary, the conversation is about finding the orbital period of two planets orbiting a star, using the equation mv^2/r=GMm/r^2+Gmm/(2r)^2. The person is asking for help in finding the correct answer.
  • #1
marshall104
13
0
The figure shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter.
This is the equation eq. I used:

mv^2/r=GMm/r^2+Gmm/(2r)^2

This is what I came up with but it is not the right answer. Where did I go wrong?

sqrt4pi^2/G(M+m)*r3/2

Any help would be great!
 
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  • #2
marshall104 said:
The figure shows two planets of mass m orbiting a star of mass M. The planets are in the same orbit, with radius r, but are always at opposite ends of a diameter.
This is the equation eq. I used:

mv^2/r=GMm/r^2+Gmm/(2r)^2

This is what I came up with but it is not the right answer. Where did I go wrong?

sqrt4pi^2/G(M+m)*r3/2

Any help would be great!


What are you trying to find ?
 
  • #3
marshall104 said:
The figure shows two planets of mass m orbiting a star of mass M.

What figure?

Zz.
 
  • #4
I'm sorry. I'm trying to find T the orbital period
 

1. How did Newton discover the theory of gravity?

Newton discovered the theory of gravity in the late 17th century through his famous thought experiment of an apple falling from a tree. He then further developed his ideas and published them in his book "Principia" in 1687.

2. What is the relationship between gravity and satellite orbits?

The theory of gravity explains that objects with mass attract each other with a force called gravity. This force is what keeps satellites in orbit around larger objects, such as the Earth, as they constantly fall towards the center of the object due to the gravitational force.

3. How do satellites move in an elliptical orbit?

Satellites move in an elliptical orbit due to the balance between their forward motion and the pull of gravity towards the center of the larger object. This results in a curved path that is constantly changing, but always follows the shape of an ellipse.

4. Are all satellite orbits perfectly circular?

No, not all satellite orbits are perfectly circular. The shape of the orbit depends on the initial velocity and distance from the larger object. Some satellites may have more elliptical orbits, while others may have nearly circular orbits.

5. How does the mass of an object affect its gravitational pull?

The mass of an object is directly proportional to its gravitational pull. This means that the larger the mass of an object, the stronger its gravitational pull will be. This is why larger objects, like planets, have a stronger gravitational pull compared to smaller objects, like asteroids.

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