Physics 101 - Astronomy - Spring 2019

Class notes for day 22, April 9, 2019

We went over material about characterizing the stars. These notes cover some of the points I made on the PowerPoint slides.

Stellar Parallax: definition - A Parsec is the distance from us that has a parallax of one arc second (parsec = pc). Figuring out how far this is involves some geometry, so it is more useful just to remember the definition below.

1 parsec = 206,265 A.U. or about 3.26 light-years (The astronomical unit A.U. is the distance between Earth and Sun, which is about 150 million kilometers.) A light-year (ly) is the distance that light travels in one year. We commonly use AU when we talk about the solar system, and pc or ly when we talk about the distance between stars.

There is a diagram in the PowerPoint, showing the location of nearby stars.
Proxima Centauri, a companion to Alpha Centauri, has a parallax angle of 0.76” (arc seconds) so the distance is 1/.76 = 1.3 parsecs.
1 parsec = 3.26 light-years, so the Alpha Centauri system is about 4.3 light-years away, or about 270,000 A.U., a typical distance between stars.
Barnard’s star is another example; it is 1.8 pc away.

An Analogy: Make a model of the Sun and Earth at 1 m distance from each other, the Sun is a yellow marble, the Earth a grain of sand, and the nearest star is 270 km away (270,000 meters, each meter represents an astronomical unit, so the star would be near St. Louis, Missouri in this model!).

The Hipparcos spacecraft mission (European Space Agency,1989-93)
This space mission, named after the ancient Greek astronomer, was the very first space mission for measuring the positions, distances, motions, brightness and colors of stars. The science of astrometry is the measurement of astronomical objects. ESA's Hipparcos satellite pinpointed more than 100,000 stars, with measurements of position that were 200 times more accurate than ever before. The accuracy is equivalent to being able to tell the height of a person standing on the Moon, seen from the Earth. The primary product from this mission was a set of stellar catalogues, The Hipparcos and Tycho Catalogues, published by ESA in 1997. These catalogues now contain data for more than 2 million stars. A short description of this data is available on the web site: “The Hipparcos Space Astrometry Mission” at http://www.cosmos.esa.int/web/hipparcos

The European Space Agency has launched another spacecraft, called Gaia, in 2015. It has measured the precise positions of more than 1 billion stars, and the distances of over 2 million of the nearer stars. For details, see their website at http://www.esa.int/Our_Activities/Space_Science/Gaia 

Inverse-Square Law for Light – means that the light is “diluted” or spread out over a larger area as it travels away from a source. I talked about the idea of light going through a square window at a distance of 1 m from a source, then at twice the distance that same light would be covering 4 squares, so the amount going through each square would be 1/4 of the amount at the closer distance 1 m. And so on. See the diagram in the Powerpoint.

Luminosity contributes to apparent magnitude, so two unlike objects at different distances may appear the same brightness (apparent magnitude). The further object must put out more light, but since it is spread out going the longer distance, the apparent brightness might be the same. See the book (or Powerpoint) for a figure of apparent magnitudes of various objects.

The absolute magnitude of a star is the apparent magnitude when viewed from 10 pc distance. Our Sun would appear to have an apparent magnitude of 4.8 if it were at 10 pc distance, so it has an absolute magnitude of 4.8

Luminosity of a star is usually compared to the luminosity of our Sun, which has one unit of solar luminosity.

Stellar Sizes range from 300 times the size of the Sun to only 0.01 times the size of the Sun. See the figures in the book for some examples.

Some stars are close enough and big enough to be seen as disks, for example Betelguese is the red star in Orion.
However, most stars look like points, so we need to deduce the size from the luminosity (based on the apparent magnitude) and the temperature by a formula:

luminosity is proportional to (radius)(squared) x (temperature)(4th power)

Antares is 300 times the size of the Sun. It would reach almost the distance to the orbit of Mars if it replaced the Sun in our solar system. There are very few stars this big. Small stars (dwarfs) range from the size of the Sun to only 0.01 times the size of the Sun, which is about the size of the Earth.