University of Colorado Boulder ASEN 6008 Interplanetary Mission Design Spring 2015 Kate Davis Real Life 1

University of Colorado Boulder  Mission designers are focused on one primary task: 1. Satisfy the scientists (or other customer) A.Maximize the delivered mass i.Minimize the launch energy ii.Minimize the arrival velocity iii.Minimize the deep space fuel costs B.Minimize the transfer duration C.Minimize risk 2

University of Colorado Boulder  Your boss asks you to give a reasonable estimate for the ΔV required to enter orbit about Uranus. ◦ You already know the Vis-Viva equation and can relate a V ∞ to an orbit insertion ΔV.  Let’s assume r p = 50,000 km; r a = 10 6 km. ◦ She gives you 5 minutes to answer.  0 th order estimate ◦ She gives you 15 minutes to answer  1 st order estimate ◦ She gives you 1 hour to answer  Low-fidelity estimate ◦ She gives you 1+ days to answer  High-fidelity estimate 3

University of Colorado Boulder  How would you provide an estimate of the orbit insertion ΔV at Uranus given:  5 minutes?  Keep it very simple: ◦ Planar ◦ Ignore C 3 ◦ Ignore TOF 4

University of Colorado Boulder  How would you provide an estimate of the orbit insertion ΔV at Uranus given:  5 minutes?  Guess the arrival V ∞ ◦ If you don’t have a better guess, go with 0 km/s ◦ rp = 50,000 km ◦ 0 km/s  367 m/s orbit insertion ◦ “Absolute minimum of 367 m/s!” ◦ (and then multiply it by 4) “Probably more like 1300 m/s” ◦ If you had a better guess: 5

University of Colorado Boulder  How would you provide an estimate of the orbit insertion ΔV at Uranus given:  15 minutes?  Estimate the best possible path from Earth or another planet to Uranus. ◦ Now we can consider gravity assists! ◦ Question: is it possible to get a V ∞ of 0 km/s? ◦ Question 2: if we had a perfect alignment, would we want to get the BIGGEST boost possible from Jupiter or another planet? 6

University of Colorado Boulder  Ignoring timing, launch, orbits, and TOF considerations, what is the “perfect” planetary alignment to minimize orbit insertion ΔV? 7 Sun Planet 1 Uranus’ Orbit Well, a Hohmann Transfer!

University of Colorado Boulder  Can a gravity assist from Planet 1 improve the transfer at all? ◦ Only TOF or non-coplanar accommodations. 8 Sun Planet 1 Uranus’ Orbit Well, a Hohmann Transfer! If you flew by “harder” you could: -Raise Ra -Lower Rp -Change inc -Change AOP All of these generally increase V ∞ If you flew by “harder” you could: -Raise Ra -Lower Rp -Change inc -Change AOP All of these generally increase V ∞ To minimize V ∞ at arrival, you want to maximize the perihelion radius. The way to do that is to place the final gravity assist at periapse. To minimize V ∞ at arrival, you want to maximize the perihelion radius. The way to do that is to place the final gravity assist at periapse.

University of Colorado Boulder  Best possible transfers from previous orbits. 9 Uranus Saturn Jupiter

University of Colorado Boulder  Best possible transfers from previous orbits. 10 “If we fly by Saturn, then the best possible ΔV is only 418 m/s!” (multiply that by 3) “More likely, we’re talking about 1200 m/s”. “If we fly by Jupiter, then the best possible ΔV is only 548 m/s!” (multiply that by 3) “More likely, we’re talking about 1500 m/s”.

University of Colorado Boulder  How would you provide an estimate of the orbit insertion ΔV at Uranus given:  1 hour?  Generate a Pork Chop Plot from each planet to Uranus and assume that we can minimize the arrival V ∞. ◦ Now we can consider orbital variations and phasing. 11

University of Colorado Boulder 12

University of Colorado Boulder  Best possible transfers from previous orbits.  This is an improvement! But man, that’s a long mission ◦ 20 years? Not in my boss’ career span “The best you can possible do using a Jupiter Gravity Assist is a ΔV of 587 m/s” (double that to account for reducing TOF) “We’re talking along the lines of 1100 m/s” 13 Min V ∞ ~ 2.6 km/s ΔV ~ 587 m/s

University of Colorado Boulder 14 Reduce TOF to 11 years. V ∞ : 5.5 km/s Probably want it down to 7 years or less. V ∞ : 8 km/s… Reduce TOF to 11 years. V ∞ : 5.5 km/s Probably want it down to 7 years or less. V ∞ : 8 km/s…

University of Colorado Boulder “The best you can do with a Jupiter Gravity Assist, no Saturn Gravity Assist, and low TOF is a ΔV of m/s” (add more margin to account for getting to Jupiter!) 15

University of Colorado Boulder  Then of course if you have 1+ week, you can design a full interplanetary mission and answer their question more confidently. 16

University of Colorado Boulder  One of the points I’m working on making: you don’t want to depart a planet going too fast. 17 The optimal Uranus arrival conditions required an outbound V ∞ departing Jupiter of about 4 km/s.