Stellar Distances

3.1. Define parsec.
The distance from Earth of a star that has a parallax angle of one second. The word parsec comes from one parallax angle per second and it is usually abbreviated to pc. 

3.2 Describe the stellar parallax method of determining a distance to a star.


The parallax angle can be measured by observing changes in the star's position over a period of a year. We can use trigonometry  to work out the distance of the star from the Earth (as we know the distance between the Earth and the Sun).

The parallax angle and distance from the Earth to star are always inversely proportional.

Units:

1. The distance from the Earth to the Sun can be described as 1 Au (Astronomical Unit) = 1.5 x 10^11m.
2. Calculations show that a star with an parallax angle of 1 second of arc must be 3.08 x 10^16m away (3.26 light years or ly).
3. This distance is defined as parsec (see above) 

3.3 Explain why the method of stellar parallax is limited to measuring stellar distances less than several hundred parsecs.
The parallax angles for stars are greater distances are too small to measure accurately. The smallest -parallax angle that can currently be measured is 0.01 arc-second. The limitation on ability to measure the angle accurately therefore, limits the method in that it can only be used to measure the distances of close stars.
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3.4 Solve problems involving stellar parallax

3.5 Describe the apparent magnitude scale.

• Apparent magnitude: Its apparent brightness viewed by an observer on Earth.
• Each magnitude is 2.51 times brighter than the next.
• The Ancient Greeks: classified stars according to brightness, 1 = the brightest, 6= the dimmest magnitude, m=1. A magnitude 1 star was first considered to be twice as bright as a magnitude 2 star, which was in turn as bright as a magnitude 3 star and so on (simple logarithmic scale). 
• A magnitude 1 star = 2.51^5 = 100 times brighter than a magnitude 6 star.
• Modern magnitude scale: Star of brightness 2.52 x 10^-8 Wm^-2 is given an apparent magnitude of 0.
• Note: Apparent brightness has unit whereas apparent magnitude is a ratio.
• Apparent magnitude of star depends on LUMINOSITY and its DISTANCE FROM EARTH.
• The brightest objects have MORE NEGATIVE values whereas the dimmest objects are MORE POSITIVE.

3.6 Define absolute magnitude

Absolute magnitude (M) the apparent magnitude of a star if it were 10 parsecs (pc) from Earth.

Most stars are further away than only 10 pc from Earth therefore they would appear brighter if they were only 10pc away. Therefore for most stars their absolute magnitudes are more negative than their apparent magnitudes (more brightness in absolute).

3.7 Solve problems involving apparent magnitude, absolute magnitude and distance.
(below)
3.8 Solve problems involving apparent magnitude and apparent brightness.

Some Images and diagrams from: Heinemenn HL Physics Course Companion, IB Physics study guide by Tim Kirk