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.

Astronomy
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ISBN:9781938168284
Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher:Andrew Fraknoi; David Morrison; Sidney C. Wolff
Chapter19: Celestial Distances
Section: Chapter Questions
Problem 32E: The best parallaxes obtained with Hipparcos have an accuracy of 0.001 arcsec. If you want to measure...
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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.

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