Determining Mass of Binary Star Systems Using Center of Mass Method

In summary, the conversation discusses the use of telescopic observations to determine the masses of stars in a binary star system. The circular orbits of the two stars and their periods are given, and the center of mass is used to find the masses of the stars using formulas involving the orbital radii and the period. The chapter being studied focuses on energy, so further help is needed to understand and apply the concept.
  • #1
HasuChObe
31
0
Hi, I'm new to these forums. Gonna give the homework help section a spin =] Here's my question:

(a) About half of the visible "stars" are actually binary star systems, two stars that orbit each other with no other objects nearby. Consider the motion of the center of mass of a binary star system. For a particular binary star system, telescopic observations repeated over many years show that one of the stars (whose unknown mass we'll call M1) has a circular orbit with radius R1 = 5x10^11 m, while the other star (whose unknown mass we'll call M2) has a circular orbit of radius R2 = 9x10^11 m about the same point. Make a sketch of the orbits, and show the positions of the two stars on these orbits at some instant. Label the two stars as to which is which, and label their orbital radii. Indicate on your sketch the location of the center of mass of the system. (Do this on paper; you will not be asked to turn it in. )(c) This double star system is observed to complete one revolution in 49 years. What are the masses of the two stars? (For comparison, the distance from Sun to Earth is about 1.5x10^11 m, and the mass of the Sun is about 2x10^30 kg.) This method is often used to determine the masses of stars. The mass of a star largely determines many of the other properties of a star, which is why astrophysicists need a method for measuring the mass.

M1 and M2 are unknown. The period for one revolution is 49 years. The radius of the circular orbit of M1 is 5x10^11. The radius of the circular orbit of M2 is 9x10^11. How do I find M1 and M2 given this information?
Supposed to use center of mass to figure this one out =/ All help is appreciated.
 
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  • #2
Use what is given in the problem (1.5x10^11 m) as a circular radius of Earth's orbit.
Then using what you’ve learned and know about our local solar system to figure the circular orbit of the Sun (ignoring other planets of course) and other details; Center of Mass, periods, diagram, etc.

From doing that you should able to understand the formulas well enough to determine how to figure the given problem.
Let us know what you get
 
  • #3
-____-;; I don't know how to use the period. The chapter I'm on actually focuses on energy. More help needed!
 
  • #4
m1= ((r1+r2)^2 *(r2) (2 pi)^2) / G T^2

m2 = ((r1+r2)^2 *(r1) (2 pi)^2) / G T^2
 

FAQ: Determining Mass of Binary Star Systems Using Center of Mass Method

What is the definition of "Mass of Two Binary Systems"?

The mass of two binary systems refers to the total mass of two objects or bodies that are in orbit around each other. These objects can be stars, planets, or any other celestial bodies.

How is the mass of two binary systems calculated?

The mass of two binary systems is calculated using Kepler's third law of planetary motion, which states that the square of the orbital period is directly proportional to the cube of the semi-major axis of the orbit. By measuring the orbital periods and distances of the two objects, we can calculate their combined mass.

Why is the mass of two binary systems important?

The mass of two binary systems is important because it can provide valuable information about the objects and their orbits. It can also help us understand the formation and evolution of the system, as well as the dynamics of their interactions with each other.

What factors can affect the mass of two binary systems?

Several factors can affect the mass of two binary systems, including the distance between the two objects, their sizes, and their compositions. The gravitational pull of nearby objects can also have an impact on the mass of the system.

How do scientists study the mass of two binary systems?

Scientists study the mass of two binary systems by observing their orbital periods and distances using telescopes and other instruments. They also use computer simulations and mathematical models to analyze the data and make predictions about the system's behavior.

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