Masses of binary system (quick q)

In summary, when given the period of a binary star system, rest wavelength, and max doppler shift, the orbital speed of the star can be calculated using the doppler equation. To find the combined mass of the stars in solar units using the simplistic model of a circular orbit, the modified kepler 3rd law can be used. To obtain the semi major axis, the orbital speed can be multiplied by the period in seconds. Alternatively, the velocity can be calculated using the equation Velocity = 2 Pi r / Period.
  • #1
Jhero
1,052
0
I have this problem:

Given is period of an eclipsing binary star system is 34 days, rest wavelength is 6563 angstroms while max doppler shift of 2.34 angstroms

I used the doppler equation to figure out the orbital speed of the star; now the question says to use the simplistic model of being in a circular orbit about the other star , calculate the sum of the masses of the stars in solar units.

I know I have to use the modified kepler 3rd law to find the combined mass but how do i get 'a' or semi major axis? Do I just multiply the orbital speed by the period in seconds to get this?

thanks
 
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  • #2
Hi. can't you use the fact that
Velocity = Circumference/ Period = 2 Pi r / Period
 
  • #3


Hi there,

Great job using the Doppler equation to find the orbital speed of the star. To calculate the sum of the masses of the stars in solar units, you will indeed need to use the modified Kepler 3rd law. To find the semi-major axis, you can use the equation a = (GM T^2/4π^2)^(1/3), where G is the gravitational constant, M is the combined mass of the stars, and T is the orbital period in seconds.

So, to find the combined mass, you will first need to convert the orbital period from days to seconds. Then, plug in the values for a and T into the equation and solve for M. This will give you the combined mass of the stars in terms of solar units.

I hope this helps! Let me know if you have any other questions. Good luck!
 

FAQ: Masses of binary system (quick q)

What is a binary system?

A binary system is a pair of astronomical objects that are gravitationally bound and orbit around a common center of mass. These objects can be stars, planets, or other celestial bodies.

How are the masses of a binary system determined?

The masses of a binary system can be determined by studying the orbital motion of the two objects. By measuring the period and separation of their orbits, as well as their relative velocities, scientists can calculate the masses using Kepler's laws of planetary motion and Newton's laws of gravity.

Why are binary systems important in astronomy?

Binary systems provide valuable information about the masses and properties of astronomical objects. They also allow us to study the effects of gravitational interactions and how they shape the evolution of these objects.

Can the masses of a binary system change over time?

Yes, the masses of a binary system can change over time due to various factors such as mass transfer between the two objects, tidal interactions, and supernova explosions. These changes can affect the stability and evolution of the system.

Do all binary systems have equal mass objects?

No, binary systems can have objects of different masses. In some cases, one object may be significantly more massive than the other, such as in a binary star system where one star is a giant and the other is a white dwarf. In other cases, both objects may have similar masses, such as in a binary star system with two main sequence stars.

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