ASTR 310 Problem Set 04: Weighing the Sirius AB System with Kepler’s Third Law

Problem set for Unit 4.

Problems

1. Unit conversion 15 points

The Sirius AB system has an orbital period of 50.13 years and a semimajor axis of 19.78 AU (standard published visual-binary orbital elements). Convert both quantities to SI units (seconds and meters).

2. Total mass from Kepler’s third law 20 points

Using your Problem 1 results and the generalized Kepler's third law, compute the total mass of the Sirius AB system in solar masses.

3. Comparison to individually measured masses 15 points

Sirius A's individually measured mass is about 2.063 M⊙ and Sirius B's (from ASTR230, independently verified) is 1.018 M⊙. Compute the percent agreement between the sum of these and your Problem 2 answer.

4. Escape velocity contrast 15 points

Using Sirius B's mass (1.018 M⊙) and radius (0.008098 R⊙), compute its surface escape velocity, and compare it (as a ratio) to Sirius A's surface escape velocity (M = 2.063 M⊙, R = 1.711 R⊙). Explain the physical reason for the large contrast, referencing Lecture 07.

Due and Scope

Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.

OpenStax Companion Reading

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 3.1-3.3.

References and Data Sources