Finding masses of Sirius A and B from orbital period and angular semimajor axes

[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.

 

[diazona]

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.

 

[leonne]

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

 

[diazona]

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

 

[leonne]

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