# What Are the Masses and Uncertainties of Sirius A & B?

• leonne
In summary, the distance to the Sirius system is 2.64+-0.01 pc, and the masses of Sirius A and B are 4.93+-0.06 and 1.41+-0.02 solar masses, respectively. The uncertainties in the masses are .01/100.
leonne

## Homework Statement

Sirius is a visual binary with an orbital period P = 49.94 yr. Sirius A (the bright
star) has an angular semimajor axis of ~ A = 2.4190'", while Sirius B (the fainter
star) has ~ B = 5.191". The distance to the Sirius system is 2.64+-0.01 pc. What
are the masses of Sirius A and B? What are the uncertainties in the masses?

## Homework Equations

M=m1+m2=(4pie^2 d^3 a^3)/Gp^2

## The Attempt at a Solution

my question is for the distance would i just put 2.64 pc or need to do something with the +- .001? and the uncertainties in masses would be .01/100? Also is this question asking for mass of each star or total? Not sure how you can find the individual mass with this data.

To look at it one way, there are really four numbers this question asks you to calculate:
- the mass of Sirius A
- the mass of Sirius B
- the uncertainty in the mass of Sirius A
- the uncertainty in the mass of Sirius B
You can calculate the first two (the masses themselves) first, using 2.64 pc as the distance to the system. Then after you've done that, you can go back and find the uncertainties in the masses. In order to do that, you will need to use the uncertainty in the distance, which is 0.01 pc.

Note that the question gives you the angular size of each star's orbit around their common center of mass. That is the information you need to solve for the individual masses.

hey thanks yea i figured it out but having a problem finding center of mass M=m1+m2=(4pie^2 d^3 a^3)/Gp^2 when i plug everything to find center of mass get a huge number and should be only 3 solar mass once i find that i can find velocity then find mass of the single star

If you show the details of your calculation, we might be able to help you fix it. (Also, some punctuation would be much appreciated )

lol ok, well was saying that my given data is a little different from what wiki had. like on wiki they had period as 94.9 and my angular semimajor axis is a little bigger, so it should be good thxs. Now just need to figure out last problem something with Taylor expansion and figuring out fractional uncertainty on the total mass fM from distance, i guess to make a formula or something

## 1. What is the mass of Sirius A and B?

The mass of Sirius A is approximately 2.02 solar masses, while the mass of Sirius B is about 0.978 solar masses.

## 2. How was the mass of Sirius A and B determined?

The masses of Sirius A and B were determined using a technique called astrometry, which involves measuring the gravitational influence of the two stars on each other. This data was combined with other observations, such as the stars' orbital period and spectroscopic data, to calculate their masses.

## 3. Why is it important to accurately determine the masses of Sirius A and B?

Accurately determining the masses of Sirius A and B allows us to better understand the evolution and properties of these stars. It also provides valuable information for studying binary star systems and testing theories of stellar evolution.

## 4. Have the masses of Sirius A and B changed over time?

Yes, the masses of Sirius A and B have changed over time. As the stars age and evolve, they lose mass through stellar winds and other processes. However, the changes in their masses are relatively small and have a minimal impact on their overall properties and behavior.

## 5. Are there any uncertainties or limitations in the determination of the masses of Sirius A and B?

Yes, there are some uncertainties and limitations in the determination of the masses of Sirius A and B. These include measurement errors, as well as assumptions and simplifications made in the calculations. However, multiple methods and observations are used to determine the masses, which helps to minimize these uncertainties.

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