ASTR 310 Problem Set 06: A Hohmann Transfer to Venus and the Sun-Earth vs. Sun-Jupiter L1 Points

Problem set for Unit 6.

Problems

1. Transfer orbit setup 15 points

Design a Hohmann transfer from Earth (a = 1.0000 AU) to Venus (a = 0.7233 AU). Compute the transfer orbit's semimajor axis and its perihelion and aphelion distances.

2. Both burns 20 points

Compute both required velocity changes (Δv1 leaving Earth's orbit, Δv2 arriving at Venus's orbit) using the vis-viva equation, and compute the total mission Δv.

3. Transfer time 15 points

Compute the one-way transfer time in days, and compare it (as a ratio) to the Earth-Mars transfer time computed in Lab 06, explaining why the Venus transfer is shorter.

4. Sun-Jupiter L1 20 points

Using r_L1 ≈ R(m2/3m1)^(1/3), compute the Sun-Jupiter L1 distance (Jupiter's orbital radius is 5.2044 AU) and compare it (as a ratio) to the Sun-Earth L1 distance from Lecture 12/Lab 06. Explain why the ratio is much larger than the simple ratio of Jupiter's to Earth's orbital radii alone.

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 3.4-3.6.

References and Data Sources