Question

Describe the parallax method for finding the distance to stars. What are the advantages and disadvantages of this method?

The apparent magnitude of the Sun is -26.7 and its absolute magnitude is +4.83. The star Sirius has an apparent magnitude of -1.46 and an absolute magnitude of +1.5. Antares has an apparent magnitude of +0.92 and an absolute magnitude of -5.3. Which one of these three objects is intrinsically the brightest? Explain what these numbers mean and how these three objects compare.

The luminosity of Vega is 60 times more than that of our Sun. Knowing the Sun’s luminosity to be 4 x 10²⁶ W, what is Vega’s luminosity? How many 100 W light bulbs do you need to equal Vega’s luminosity? Show all the work for both answers.

Answer 1

1]

Parallax method can be used for roughly measuring the distance of a given star from the earth by measuring how much the star travels in a given time in our reference frame. This measurement is in terms of the angle the star subtends from the initial and final position.

From this, the distance is calculated as:

where the angle is in arcseconds and distance d is the parsecs.

Disadvantages of this method:

1 arc second is 0.0002777 degrees

so, the angles are very small and the limitations to this measurement is about 0.01 arcseconds with best telescopes.

this thereby limits the farthest star to be detected.

2]

The brightest star is the one with smallest value of apparent magnitude. This corresponds to Antares since it has a negative absolute magnitude.

The smallest apparent magnitude indicates how close the object is to the observer. Since our sun has the smallest (negative of 26.7) therefore the sun is closest to us.

Absolute magnitude is a way of objectively determining how bright the object is when placed at a distance of 10 parsecs.

It is the measure of the apparent magnitude of the object when its distance is made 10 parsecs.

3]

The luminosity of Vega will be:

I = 60(4 x 10²⁶) = 2.4 x 10²⁸ W

power of one lightbulb = 100 W

so, number of 100 watt light bulbs required to give the same luminosity is:

n = 2.4 x 10²⁸ /100 = 2.4 x 10²⁶ .