Stellar Properties From Afar

by Mee Wong-u-railertkun, Nathan Baskin, John Pharo, David Vartanyan

Credit: apod.nasa.gov Info about this picture is presented below.

We present the solution to the first question from the worksheet "Stellar Properties From Afar."

We are given the following information about the sun,
1) The angular diameter of the sun is 0.5 degrees.
2) The astronomical unit (AU), distance between the Earth and the Sun, is approximately 1.5 * 10^13 cm.

Part (a) - Find the radius of the Sun in centimeter.

If we draw a circle around the Earth with the radius of one AU by going right through the Sun, the diameter of the sun is part of the circumference. Since the total angle of a circle our its center is 2*pi or 360 degrees, we can relate the known informations given by the question to the unknown value.

After compare with the "official" value of the sun radius, which is approximately 6.95*10^10 cm, our answer is 94.5% of the official value which is amazingly good.

Part (b) - Find the AU in solar diameters to 1 significant figure (memorize this handy value)

We can rearrange the relationship above to write AU in term of the solar radius.

Part (c) - Find the mass of the Sun according to Newton's version of Kepler's third law.

Kepler's third law relate period with the distance between a planet and a star.

Newton came to fix and change the proportional sign to equal sign by finding the constant.

In most case, including the case between the Earth and the Sun, mass of a planet is much smaller than mass of the stas. Thus, the equation can be reduced to,

Period of the Earth is approximately 365 days or 31536000 seconds. We can calculate the estimated mass of our sun,

The official value of the mass of the sun is approximately 1.988*10^30 kg. Thus, our answer is 100.95% of the official value.

Acknowledgement

We thank WolframAlpha for offering the official values of the Sun's radius and mass. All equations are made by Online LaTex Equation Editor.

Info about the picture of the Sun above.

The image is called "A Complete Solar Cycle from SOHO." The sun goes through the eleven-year cycle. The cycle is caused by the changing magnetic field of the Sun, and varies from solar maximum when solar phenomena - sun spots, coronal mass ejection, flare phenomena - are most frequent, to the solar minimum, when those activities are rare. In the picture, the Sun is taken picture from 1996 to 2006. During 2001, the Sun is at its maximum while at 1996 or 2006, the sun is relatively "quieter." The images are taken in extreme ultraviolet light by the SOHO spacecraft.