Characterizing Stars
The stars Every star you see in the sky is a large hot ball of gas like our star the Sun. Each one possibly making up a solar system with planets and debris orbiting around them. Stellar parallax can be used to find out how far away a star is from us. The closest star to us is called Proxima Centauri, it is about 25 trillion miles away. Light from this star takes about four years to reach us.
Stellar parallax Parallax is the viewing of an object from two different locations. This will cause the object to appear in different places compared to a background. The angle between the two apparent locations is called the parallax angle. The closer the object is the larger the parallax angle will be.
Calculating distance using parallax The distance from earth to a star can be calculated using the equation: d = 1 p In this equation d is distance in units of parsecs and p is the parallax angle in units of arcseconds. In a circle there is 360 degrees or 24 hours of arc. Each h of arc can be spit into 60 arcminutes, and each m of arc can be split into 60 arcseconds.
Example The nearest star to us is observed to have a parallax angle of 0.77 arcsec. How far away is the star in parsecs and light years? (1 pc = 3.26 ly) d = 1 p d = 1 0.77arcsec d = 1.3 pc d = 1.3 pc x 3.26 ly 1 pc = 4.24 ly
The brightness of a star In astronomy we refer to a stars brightness as its magnitude. There are two types of magnitudes when it comes to an objects brightness. One is called apparent magnitude and the other absolute magnitude.
Apparent magnitude Apparent magnitude denoted by lower case m, is the brightness of a star as seen from Earth. This apparent magnitude doesn't take into account how far away the star is. Therefore apparent magnitude is not the stars actual brightness.
Apparent magnitude scale The apparent magnitude scale has positive and negative numbers. The bigger the positive number the dimmer the object. The bigger the negative number the brighter the object.
Inverse-square law The same amount of radiation must illuminate a larger area as it gets further from the source. This is why an object looks dimmer the further you are from it. Brightness decreases inversely with the square of the distance from the source of light. This is also known as the inverse-square law. I 1 d 2
Example You are a certain distance d away from a light source and measure the brightness to be of a certain intensity I. How would the intensity change if you are (a) twice, and (b) half as far from the source?
Example continued (a) I 1 d 2 I 1 (2d) 2 I 1 4d 2 Therefore if the distance is doubled the intensity will be one fourth the original, or four times dimer.
Example continued (b) I 1 d 2 I 1 ( 1 2 d)2 I 1 1 4 d2 = 4 d 2 Therefore if the distance is halved the intensity will be four times the original, or four times as bright.
Absolute magnitude Absolute magnitude takes into account that there are different stars at different distances from us. It also uses the same scale as apparent magnitude. If the apparent magnitude and distance of a star is known, that stars absolute magnitude can be calculated. Absolute magnitude (M), is the brightness each star would have at a distance of 10 pc (32.6 ly).
Calculating absolute magnitude To calculate absolute magnitude use the equation: M: absolute magnitude M = m 5 log d 10 m: apparent magnitude d: distance in parsecs
Example The star Proxima Centauri is 1.3 pc away from Earth and has an apparent magnitude of +11.1. What is its absolute magnitude? M = m 5 log d 10 M = 11.1 5 log 1.3 10 M = 11.1 5 0.886 M = 11.1 ( 4.4) M = +15.5
A stars color and temperature A stars color and surface temperature are related. A red stars have the lowest surface temperature, while a blue stars have the highest surface temperature.
Types of stars Stars come in many different sizes, brightness, and colors. There are four major types of stars. White dwarfs, main sequence stars, giants, and super gaints.