# What is the Period of Revolution for a Triple Star System?

• chaose
In summary, a triple star system consists of two stars of mass m each orbiting around a central star of mass M in a circular orbit of radius r. The period of revolution for the two orbiting stars can be derived using Kepler's Third law and the net gravitational force exerted by the other two stars, resulting in the expression T^2 = (16pi^2 * r^3)/(G*(4M+m)).
chaose
A triple star system consists of two stars each of mass m revoling in the same circular orbit of radius r around a central star of mass M. The two orbiting stars are always at opposite ends of a diameter of the orbit. Derive an expression for the period of the revolution of the stars.

I don't understand this problem that well. Any hints?

I thought that if the two stars are at opposite ends of the orbit, won't the gravitational forces from one cancel out the forces from the other star?
Then won't the period just be Kepler's Third law?

T^2 = (r^3)*(4pi^2)/(GM), G = universal gravitational constant, M = mass of central star, T = period of revolution, r = radius of the orbit, pi = 3.14159...

The force on each orbiting star is the sum of the forces from the other two stars. The net force on the central star will be zero, so it is stationary at the center of the motion of the other two stars. You can do this as a basic centripetal force problem if you get the forces right.

thanks, I believe I got it now.

My end result was
T^2 = (16pi^2 * r^3)/(G*(4M+m))

## 1. What causes weird gravitational problems?

Weird gravitational problems can be caused by a variety of factors, such as unusual mass distributions, strong gravitational fields, or the presence of multiple bodies interacting with each other.

## 2. How do you solve a weird gravitational problem?

Solving a weird gravitational problem requires a thorough understanding of Newton's laws of motion and the principles of gravitation. It also involves using mathematical equations and techniques, as well as computer simulations, to analyze the problem and find a solution.

## 3. Is it possible to encounter weird gravitational problems in everyday life?

While most people don't encounter weird gravitational problems in their daily lives, they can occur in extreme situations such as near black holes or other highly massive objects. However, the effects of these problems are usually very small and not noticeable to the average person.

## 4. Can weird gravitational problems be observed in space?

Yes, weird gravitational problems are often observed in space, particularly in the interactions between celestial bodies. For example, the orbit of Mercury around the Sun deviates slightly from what is predicted by Newton's laws, due to the influence of other planets and the Sun's strong gravitational pull.

## 5. How does Einstein's theory of relativity affect weird gravitational problems?

Einstein's theory of relativity, particularly the concept of spacetime curvature, provides a more accurate and complete understanding of gravity. It is especially important in extreme gravitational situations, such as near black holes, and can help explain some of the weird behaviors observed in these scenarios.

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