# Chapter 19

**Chapter 19 – Introduction to the Stars complete! Again, if there is anything that looks a bit dodgy, just let me know via the comments box! 🙂**

1. a) Using a diagram, show what is meant by the trigonometrical parallax of a star.

The trigonometrical parallax of a star is angle that the star appears to move from its original position. Because when we see stars, we see them as a point of light. We have no idea what distance they are. So if you stand in one place, at a certain time on a certain day in summer, you can see a star. Then, come back exactly half a year later and stand in the same place at the same time. The star will have moved a tiny amount. Measure that angle and divide into two; because the parallax angle is; a line through the Sun and the star, to a line through Earth and the apparent position of the star.

1. b) What is the meaning of the term ‘parsec’?

The word ‘parsec’ comes from **par**allax and **sec**ond of an arc. A parsec is a form of measurement, usually used to measure the distance between the Earth and stars. Using the distance between the Earth and the Sun, which is 1 Astronomical Unit, we divide it by the parallax angle. So if the angle is 2.35 arc seconds (there are 36,000 arc seconds in a degree) then 1 divided by 2.35 is 0.435… That means it is 0.435 parsecs to the star. We can then change that distance into light years by multiplying it by 3.26. Therefore it is 1.39 lightyears to the star.

1. c) The star Procyon has an annual parallax of 0.287 seconds of an arc. What is it’s distance in (i) parsecs (ii) lightyears?

1/0.287 = 3.484… parsecs

3.484 x 3.26 = 11.359 lightyears.

2. a) What is the brightness ratio between two stars A and B, whose apparent magnitudes are respectively 3.3 and 4.3?

Star 1= 3.3 Star 2= 4.3

The difference is 1, and the ⁵√100 is 2.512.

2.512 to the power of 1 (difference) is 2.512, so Star A is 2.512 times brighter than Star B.

2. b) A star magnitude 2.1 lies at a distance of 10 parsecs. What is its absolute magnitude?

M= 5 + m – 5logD M= ?

M= 5 + 2.1 – (5 x log 10) m= 2.1

M= 5 + 2.1 – 5 D= 10 (log 10 = 1)

M= 2.1 magnitude

2. c) A star 100 parsecs away has an apparent magnitude of 7. What is its absolute magnitude?

M= 5 + m – 5logD M= ?

M= 5 + 7 – (5 x log 100) m= 7

M= 5 + 7 – 10 D= 100 (log 100 = 2)

M= 2 Magnitude.

3. a) What is meant by the photographic magnitude of a star?

The photographic magnitude of a star is the colour of the star. With certain stars, with notice of size and distance of the star, the colour with have a higher or lower magnitude. If a blue star was photographed next to a red one, then the blue star would have a larger photographic image; whilst the red one would be fainter and smaller. The magnitude is measured by the size of the photographic image.

3. b) Define the term ‘colour index’.

The colour index is a simple numerical index for the different colours of stars, which also corresponds to their temperature. For instance a red star like Rigel has a colour index of -0.66, whilst a more brilliant star such as Sirius has a colour index of -0.05.

3. c) Two stars, A and B, have colour indices which are respectively +2.3 and -1.9. What does this tell you about the colours of those stars?

Star A has a colour indices of 2.3, meaning it must be more blue in colour, whilst Star B has a colour indices of -1.9, which means it must be more red in colour.

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