Calculating the Distance of a Parallax Triple Stellar System

[MathematicalPhysicist]

The question:
A triple stellar system, showing a parallax of 0.01 arcsecond, is composed of a binary system,
with a distance between the two stars of 0.2 AU, and a third star, at a distance of 90 AU from
the binary. This system is observed in the optical (wavelength of 55000 Angstram) with a 1 meter telescope.
a. What is the distance of this system ?
b. How many stars will actually be seen when using a space-based telescope ?
c. How many stars will be seen when using a ground-based telescope, where the typical seeing
is 1 arcsecond ?


My attempt at solution
a. Well, $$\theta=0.01[arcseconds]$$, $$D=\frac{\lambda}{\theta}$$ where lambda is the wavelenghth given in the brackets, and D is the distance of this stellar system from earth.

Don't know how to do b. and c., any advice?

Thanks in advance.

 

[anathema]

I would like to provide some insights and answers to your questions.

a. To calculate the distance of this system, we can use the formula D = 1/p, where D is the distance in parsecs and p is the parallax in arcseconds. Substituting the given values, we get D = 1/0.01 = 100 parsecs. Therefore, the distance of this system is 100 parsecs.

b. When using a space-based telescope, we can expect to see all three stars in the system. This is because a space-based telescope is not limited by atmospheric distortion and can provide a clear and detailed image of the system.

c. When using a ground-based telescope with a typical seeing of 1 arcsecond, we can only see the binary system. This is because the third star, which is at a distance of 90 AU, will not be resolved due to the limitations of the telescope's resolution. The seeing of 1 arcsecond means that the telescope can only distinguish objects that are at least 1 arcsecond apart. As the third star is only 0.2 AU away from the binary system, it will appear as one single object and cannot be resolved by the telescope.

I hope this helps to answer your questions. If you have any further doubts or need more clarification, please feel free to ask.

 

[nlightner]

a. To calculate the distance, we can use the parallax formula: d = 1/p, where d is the distance in parsecs and p is the parallax angle in arcseconds. In this case, p = 0.01 arcseconds, so the distance would be 100 parsecs.

b. When using a space-based telescope, all three stars in the triple stellar system will be visible since the telescope is not limited by atmospheric distortion or seeing.

c. When using a ground-based telescope with a typical seeing of 1 arcsecond, only the binary system will be visible. The third star, which is at a distance of 90 AU, will not be visible due to its small angular separation from the binary system. The telescope's resolution will not be able to distinguish it as a separate star.