How Do You Calculate the Mass of a Brown Dwarf in a Binary System?

In summary, to calculate the mass of the brown dwarf in a binary system using Kepler's Third Law, we use the equation M = (4π^2/G) * (a^3/P^2) and take into account the orbital speeds of the two objects. The answer for the given question is 4.79 * 10^31 kg.
  • #1
Captain Cosmo
1
0
Hello! I'm struggling with a particular question, and have no idea where to look or seek help at the moment. It's driving me crazy! I have a feel I need to use Kepler's Third Law, but am unsure how to apply it in this situation. Here:

Suppose you observe a binary system containing a main-sequence star and a brown dwarf. The orbital period of the system is 1 year, and the average separation of the system is 1 . You then measure the Doppler shifts of the spectral lines from the main-sequence star and the brown dwarf, finding that the orbital speed of the brown dwarf in the system is 24 times greater than that of the main-sequence star.

What do I do here?!

Thank you for your time!EDIT: Never mind! I figured it out! The answer is 7.97 * 10^28 kg. I simply used a different equation. Thanks anyways, guys!
 
Last edited:
Astronomy news on Phys.org
  • #2


Hello! Kepler's Third Law states that the square of the orbital period is proportional to the cube of the average separation between the two objects. In this situation, we can use this law to calculate the mass of the brown dwarf.

First, we need to rearrange the equation to solve for mass:

M = (4π^2/G) * (a^3/P^2)

Where M is the mass of the system, G is the gravitational constant, a is the average separation, and P is the orbital period.

Plugging in the values given in the question, we get:

M = (4π^2/G) * (1^3/1^2)

M = (4π^2/G)

Now, we need to use the given information about the orbital speeds to find the mass of the brown dwarf. The ratio of the orbital speeds is equal to the ratio of the masses of the two objects.

So, we can set up the following equation:

24 = (M brown dwarf/M main-sequence star)

Solving for M brown dwarf, we get:

M brown dwarf = 24 * M main-sequence star

Now, we can substitute this value into our previous equation:

M = (4π^2/G) * (24 * M main-sequence star)

Finally, we can plug in the values for G and M main-sequence star (G = 6.67 * 10^-11 Nm^2/kg^2 and M main-sequence star = 2 * 10^30 kg) to solve for M brown dwarf:

M brown dwarf = (4π^2/6.67 * 10^-11) * (24 * 2 * 10^30)

M brown dwarf = 4.79 * 10^31 kg

So, the mass of the brown dwarf in this binary system is approximately 4.79 * 10^31 kg.

I hope this helps! Let me know if you have any further questions.
 

What is a binary brown dwarf mass?

A binary brown dwarf mass refers to the combined mass of two brown dwarfs that are orbiting around each other. Brown dwarfs are sub-stellar objects that are too massive to be considered planets, but too small to sustain nuclear fusion in their cores like stars do. When two brown dwarfs are in a binary system, their combined mass is considered the binary brown dwarf mass.

How is the mass of a binary brown dwarf determined?

The mass of a binary brown dwarf is typically determined using a variety of methods, including radial velocity measurements, astrometry, and direct imaging. Radial velocity measurements involve observing the gravitational pull of the brown dwarfs on each other, while astrometry measures the changes in their positions over time. Direct imaging involves capturing images of the brown dwarfs and using their brightness and distance to estimate their mass.

What is the average mass of a binary brown dwarf?

The average mass of a binary brown dwarf can vary depending on the specific system. However, studies have shown that the average mass range for a binary brown dwarf is between 10 and 80 times the mass of Jupiter.

Can the mass of a binary brown dwarf change over time?

Yes, the mass of a binary brown dwarf can change over time. This can occur through interactions with other objects in the system, such as other brown dwarfs or planets, which can alter the mass distribution between the two brown dwarfs. Additionally, as brown dwarfs age, they can lose mass through processes such as evaporation and cooling.

What is the significance of studying binary brown dwarf mass?

Studying binary brown dwarf mass can provide valuable insights into the formation and evolution of planetary systems. It can also help us better understand the properties and behavior of brown dwarfs, which can serve as a bridge between planets and stars. Additionally, studying binary brown dwarf mass can help us refine our understanding of gravitational interactions and dynamics in multiple body systems.

Similar threads

I Is there a difference between an ultracool dwarf and a brown dwarf？
    • Astronomy and Astrophysics
Replies
5
Views
2K
B Exploring the Binary Brown Dwarf Pair Luhman 16AB and Its Orbiting Objects
    • Astronomy and Astrophysics
Replies
6
Views
2K
I Could Brown Dwarf Sub-Dwarf Companions Host Habitable Moons?
    • Astronomy and Astrophysics
Replies
6
Views
3K
Brown dwarfs and close binary systems
    • Astronomy and Astrophysics
Replies
4
Views
1K
B Planetary debris found in white dwarf atmospheres
    • Astronomy and Astrophysics
Replies
5
Views
1K
I Early Catalog of Planet-Hosting Multiple Star (≥ 3) Systems
    • Astronomy and Astrophysics
Replies
3
Views
1K
B Could a brown dwarf passing through our solar system ignite Jupiter?
    • Astronomy and Astrophysics
2
Replies
40
Views
4K
B How to use the Binary Mass Function for exoplanets?
    • Astronomy and Astrophysics
Replies
4
Views
142
I How Big of an Object Orbiting Closer to the Sun Than Earth Could Be Overlooked?
    • Astronomy and Astrophysics
Replies
17
Views
2K
B Question re binary star systems & possible orbits
    • Astronomy and Astrophysics
Replies
11
Views
2K

Hot Threads

Recent Insights

Back
Top