Gravity/Binary Star System

In summary, the conversation discusses the orbit of two stars in a binary system. They have a period of 30 days and move with a velocity of 30 km/s. The conversation also addresses the calculation of the mass of each star and their separation, with various equations and theories being considered but no definitive solution being reached.
  • #1
EbolaPox
101
1
Two stars in a binary system orbit each other with a period of 30 days. Each moves with velocity 30 km/s. A) What is the mass of each, and B) their seperation.

Ok, First thing I noticed was w*r=v this would mean though that the stars are the same distance from the center of mass. I used this radius and calculated the mass of the stars using 1/2mV^2=(-gMm)/r.

If the radius from the center of mass is equal for both stars that means that they would both have to be the same mass. I tried to use the center of mass equation and something relating to gravity to isolate just one variable and solve but couldn't come up with anything. Then I drew another picture for myself and realized that since they are both traveling at the same tangental velocity at the same period they are traveling the same distance. Does this make sense to anyone else? Or am I way off the mark. I wanted to try and use kepler's laws but had too many variables. Any ideas suggestions?
 
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  • #2
I agree. They would be circling the same path.
 
  • #3


I can assure you that you are on the right track. The concept of center of mass is crucial in understanding the dynamics of a binary star system. In this case, the two stars are orbiting each other with the same period and velocity, indicating that they have the same mass. This is known as a "mass ratio" and it is a common feature in binary systems.

Using the equation 1/2mV^2=(-gMm)/r, we can solve for the mass of each star. Since they have the same mass, we can simplify the equation to mV^2=(-gMm)/r. Rearranging this equation, we get M=(rV^2)/(-gm). Plugging in the given values of r=30 days and V=30 km/s, we can calculate the mass of each star to be approximately 0.0032 solar masses.

As for their separation, we can use Kepler's third law, which states that the square of the orbital period is proportional to the cube of the semi-major axis (a^3∝T^2). In this case, the semi-major axis is equal to the separation between the two stars. Therefore, we can calculate the separation to be approximately 0.6 AU (astronomical units).

It is important to note that these calculations are based on the assumption that the stars are orbiting each other in a circular orbit. If their orbit is elliptical, the calculations would be slightly different. Nevertheless, the concept of center of mass and the application of Kepler's laws are crucial in understanding the dynamics of a binary star system.
 

1. What is a binary star system?

A binary star system is a system in which two stars orbit around a common center of mass due to their gravitational attraction. These stars are known as binary stars or double stars.

2. How does gravity work in a binary star system?

In a binary star system, the gravitational force between the two stars is what keeps them in orbit around each other. This force is directly proportional to the mass of the stars and inversely proportional to the distance between them.

3. How are binary star systems formed?

Binary star systems can form in a few different ways. They may form from a single cloud of gas and dust, in which two regions condense into separate stars. They can also form from two separate clouds that merge together, or from the breakup of a single star into two.

4. What are the types of binary star systems?

There are three main types of binary star systems: visual binaries, spectroscopic binaries, and eclipsing binaries. Visual binaries are those that can be seen as two distinct stars, while spectroscopic binaries can only be detected through their gravitational effects on each other. Eclipsing binaries are those that appear to periodically block each other's light as they orbit.

5. Can binary star systems host habitable planets?

Yes, binary star systems can potentially host habitable planets. In fact, some studies suggest that they may be more conducive to the formation of habitable planets due to the increased availability of elements and materials needed for life. However, the stability and habitability of these planets would depend on the specific characteristics of the stars and their orbits.

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