hw4ans - Phys 341: Homework #4 Solutions 1. (a) Recall that...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Phys 341: Homework #4 Solutions 1. (a) Recall that the center of mass is defined such that m A a A = m B a B , so we have m A m B = a B a A = 1 . 466 = 2 . 15 Since m A /m B > 1, star A is more massive than star B. (b) Recall that the distance can be determined from the parallax angle as d = 1 pc p 1 00- 1 So for p = 0 . 377 00 , we have d = 2 . 65 pc. (c) The phrase the semimajor axis of the reduced mass simply refers to the sum of the semimajor axes of the two star, a A + a B . This subtends an angle of 7 . 62 00 ; to get the corresponding length we multiply by the distance, finding a A + a B = 2 . 65 pc 7 . 62 00 180 3600 00 = 9 . 79 10- 5 pc = 3 . 03 10 14 cm The last factor on the first line converts from arcseconds to radians. Keplers Third Law now tells us the sum of the masses, m A + m B = 4 2 ( a A + a B ) 3 GP 2 = 4 2 (3 . 03 10 14 cm) 3 (6 . 67 10- 8 g- 1 cm 3 s- 2 ) (49 . 94 365 86400 s) 2 = 6 . 64 10 33 g = 3 . 34 M In the second line, the factor of 365 86400 in the denominator converts from years to seconds (86400 seconds per day, 365 days per year). Combining this with the result m B = 0 . 466 m A from part (a), we get m A (1 + 0 . 466) = 3 . 34 M m A = 2 . 28 M which then yields m B = 1 . 06 M 2. (a) For circular orbits, recall that the velocities are v A = 2 a A P = 2 P m B m A + m B a (1) v B = 2 a B P = 2 P m A m A + m B a (2) where a = a A + a B . Taking the ratio, we reproduce the result from class that the mass ratio can be determined from the velocity ratio, m A m B = v B v A = 22 . 4 km/s 5 . 4 km/s = 4 . 15 (b) From the expressions for the velocity above, we have...
View Full Document

This note was uploaded on 09/08/2008 for the course PHYS 341 taught by Professor Keeton during the Spring '08 term at Rutgers.

Page1 / 4

hw4ans - Phys 341: Homework #4 Solutions 1. (a) Recall that...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online