contestada

The figure(Figure 1) 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. Find an exact expression for the orbital period T. Hint: Each planet feels two forces. Express your answer in terms of M, m, r, and G.

Respuesta :

The expression for the orbital period is T = [tex]4\pi R^{\frac{3}{2} } / \sqrt{G(4M+m)}[/tex]

The force acting on one of the masses m by the other two is:

[tex]\frac{GMm}{R^{2} } + \frac{Gmm}{4R^{2} }[/tex]

This acts as the centripetal force and hence = mRω^2

  • A force that acts on a body moving in a circular path and directed towards the centre around which the body is moving is called Centripetal force.
  • When an object travels around a circular path with a constant speed, it experiences an accelerating centripetal force towards the centre.

So, [tex]\frac{GMm}{R^{2} } + \frac{Gmm}{4R^{2} }[/tex] = mRω^2

Solving this, we get ω = [tex]\sqrt{\frac{G(4M+m)}{4R^{3} } }[/tex]

We know that time period T = 2[tex]\pi[/tex]/ω

So , T = [tex]4\pi R^{\frac{3}{2} } / \sqrt{G(4M+m)}[/tex]

i.e. The expression for the orbital period is T = [tex]4\pi R^{\frac{3}{2} } / \sqrt{G(4M+m)}[/tex]

To know more about gravitation visit:

https://brainly.com/question/7282101

#SPJ4

Otras preguntas