A distant F0 star is 6.3 times less bright than a nearer F0 star which has a parallax of 0.2 arcsec. Calculate its distance in parsecs.

What is the total mass of a visual binary system if the average separation of the stars is 7.1 AU and their orbital period is 12 years?

A star is observed to have a parallax 0.45". Show that it is a distance of 7.2 LY away.

Which star in the HR diagram below will no longer exist in 1 Billion years? 60 Mun 10⁰ 10⁰ 10 10² 10⁰ 10 10 10 10 30 M 10 Solar Radi Lifetime 10 yrs 0.1 Solar Radius 10 Solar Radus O Centauri 30,000 10M Sirius B MAIN Bellatrix Lifetime 10 B Rigal Deneb 6M MA Achemar SEQUENCE 18yrs WHITE SUPERGIANTS Canopus Vega 10 Soler Radi Procyon B 10,000 Srius Lifetime 10 DWARFS Alar Arcturus Procyon eyon Polaris 5 Mun Liteting 10 yrs SIM 7 Cet AFG 6,000 GIANTS Centauri A Pollux Centaur B Eridani Aldebaran K Artares 61 Cyani A Betelgeuse Barnard's Star 61 Cygni B Lacalle 9352 0.3M Gliese 725 A Gliese 725 B Ross 128 Wolf 359, Proxima Centauri M DX Cancri 3.000

The Algol binary system consists of a 3.7 Msun star and a 0.8 Msun star with an orbital period of 2.87 days.  Using Newton’s version of Kepler’s Third Law, calculate the distance, a, between the two stars.  Compare that to the size of Betelgeuse (you’ll need to look that up).   Newton’s Version of Kepler’s Law:    (M1 + M2) P2 = (4p2 /G) a3                     Rearrange the equation to solve for a. Pi, p, is equal to 3.14. IMPORTANT NOTE: Google the value of G (the Universal Gravitational Constant) or look it up in your text.  NOTICE THE UNITS.  You must convert every distance and time in your equation to the same units, otherwise, you’ll get an incorrect answer.  That means you must convert distances to meters, solar masses to kilograms, and time to seconds.   When you compare your value to the size of Betelgeuse, it will also help that they are in the same units.

The star Rigel has a radial velocity r = 20.7km s-1, parallax 700 = 4.22mas, and proper motion components la= 1.67mas yr'in right ascension and us = 0.56mas yr1 in declination. What are its total proper motion, %3D %3D %3D tangential velocity, and space motion?