ASEN 5050SPACEFLIGHT DYNAMICS

Mid-Term Review, A-Train

Prof. Jeffrey S. ParkerUniversity of Colorado – Boulder

Lecture 27: Mid-Term Review, A-Train 1

Announcements• Homework #7 is due!

• HW 8 will be released Wednesday.

• Mid-Term handed back Wednesday (the grading is almost done…)

• Reading: Chapter 12

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Schedule from here out

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• 10/27: Three-Body Orbits• 10/29: General Perturbations (Alan)• 10/31: General Perturbations part 2

• 11/3: Mid-Term Review, A-Train• 11/5: Interplanetary 1• 11/7: Interplanetary 2

• 11/10: Entry, Descent, and Landing• 11/12: Low-Energy Mission Design• 11/14: STK Lab 3

• 11/17: Low-Thrust Mission Design (Jon Herman)• 11/19: Finite Burn Design• 11/21: STK Lab 4

• Fall Break

• 12/1: Constellation Design, GPS• 12/3: Spacecraft Navigation• 12/5: TBD

• 12/8: TBD• 12/10: TBD• 12/12: Final Review

Schedule from here out• Our last lecture will be Friday 12/12.

– Final review and final Q&A. – Showcase your final projects – at least any that are finished!

• Final Exam– Handed out on 12/12– Due Dec 18 at 1:00 pm – either into D2L’s DropBox or under my door.

• I heartily encourage you to complete your final project website by Dec 12th so you can focus on your finals. However, if you need more time you can have until Dec 18th. As such the official due date is Dec 18th.

• The final due date for everything in the class is Dec 18th - no exceptions unless you have a very real reason (medical or otherwise - see CU's policies here: http://www.colorado.edu/engineering/academics/policies/grading). Of course we will accommodate real reasons.

• If you are a CAETE student, please let me know if you expect an issue with this timeframe. We normally give CAETE students an additional week to complete everything, but the grades are due shortly after the 18th for everyone. So please see if you can meet these due dates.

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Final Project• Get started on it!

• Worth 20% of your grade, equivalent to 6-7 homework assignments.

• Find an interesting problem and investigate it – anything related to spaceflight mechanics (maybe even loosely, but check with me).

• Requirements: Introduction, Background, Description of investigation, Methods, Results and Conclusions, References.

• You will be graded on quality of work, scope of the investigation, and quality of the presentation. The project will be built as a webpage, so take advantage of web design as much as you can and/or are interested and/or will help the presentation.

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Final Project• Instructions for delivery of the final project:

• Build your webpage with every required file inside of a directory. – Name the directory “<LastName_FirstName>”– there are a lot of duplicate last names in this class!– You can link to external sites as needed.

• Name your main web page “index.html”– i.e., the one that you want everyone to look at first

• Make every link in the website a relative link, relative to the directory structure within your named directory.

– We will move this directory around, and the links have to work!

• Test your webpage! Change the location of the page on your computer and make sure it still works!

• Zip everything up into a single file and upload that to the D2L dropbox.

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Space News

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• It’s looking like Space Ship 2’s feathering system was deployed while accelerating through Mach 1, causing the disintegration.

• Rosetta’s Philae lander prepping for its big descent in 9 days!

ASEN 5050SPACEFLIGHT DYNAMICS

Mid-Term Exam

Prof. Jeffrey S. ParkerUniversity of Colorado – Boulder

Lecture 27: Mid-Term Review, A-Train 8

Mid-Term Exam

Lecture 27: Mid-Term Review, A-Train 9

• Problem 1

• Common errors:– Since this isn’t a circular orbit, the DT is not half of the

orbital period. Though the Delta-nu is indeed 180 deg.

Mid-Term Exam

• Hard way: generate the two-body orbit and map the latitude:

Lecture 27: Mid-Term Review, A-Train 10

?

Mid-Term Exam

• Problem 1 solution

• Easy way (and precise):– Argument of latitude: u = ω + ν– At ascending node: u = 0 deg– At descending node: u = 180 deg– ω = 310 deg– At ascending node: ν = -310 deg = 50 deg– At descending node: ν =-130 deg = 230 deg

– Compute time past periapse for both– Delta-t = 1.138 hours

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Quadrant Checks! Ascending Descending

Mid-Term Exam• Problem 2

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Mid-Term Exam• Problem 2

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Periapsis Range: 5473.0 km

Mid-Term Exam• Problem 2

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Mid-Term Exam• Problem 2

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Use eccentricity and semi-major axis, and find the eccentric anomaly needed to make radius = 6378.1363 km. Convert to TimePastPeriapse. And also compute TimePastPeriapse of initial state. We find: Time past periapse of initial state: -2049.99566 secTime past periapse of impact: -676.70889 secDuration of time to impact: 1373.28677 sec = 0.38147 hours

Quadrant Checks!

Mid-Term Exam• Problem 2

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The missile will strike the surface traveling 8811.91852 m/s in velocity

Mid-Term Exam• Problem 3

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Mid-Term Exam• Problem 3

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Mid-Term Exam

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C/W Equations: Algorithm 48

Mid-Term Exam• Problem 3

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Mid-Term Exam• Problem 3

• omega: 0.00114400182253 rad/s

• Satellite A will be located at a position of [0.0, 0.0, 80.8050388] in meters, after 7 minutes, relative to Shuttle

• Satellite B will be located at a position of[79.17972504, 142.440310957, 0.0] in meters, after 7 minutes, relative to Shuttle

• Satellite A will have a velocity relative to the shuttle of[0.0, 0.0, 0.177354562] in m/s, after 7 minutes

 • Satellite B will have a velocity relative to the shuttle of

[0.369764446, 0.2188365, 0.0] in m/s, after 7 minutes

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Mid-Term Exam• Problem 3

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Mid-Term Exam• Problem 3

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Mid-Term Exam• Problem 3

• Satellite A's state relative to Satellite B at t=7 minutes, in meters and m/s, before executing any maneuver (A-B):– x0: -79.179725045 m– y0: -142.440310958 m– z0: 80.8050388697 m– vx0: -0.369764446945 m/s– vy0: -0.218836500483 m/s– vz0: 0.17735456256 m/s

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Mid-Term Exam• Problem 3

• What velocity is NEEDED? Equation 6-66

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t = 13 min = 780 sec

Mid-Term Exam• Problem 3

• What velocity is NEEDED? Equation 6-66

• The velocity that Satellite A needs to obtain (m/s):• vx: 0.00953422198546 m/s• vy: 0.247527429082 m/s• vz: -0.0745206696574 m/s

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Mid-Term Exam• Problem 3

• What CHANGE in velocity is needed?

• The Delta-V impulse that A has to perform, in m/s relative to B:

• Delta-Vx: 0.37929866893 m/s• Delta-Vy: 0.466363929565 m/s• Delta-Vz: -0.251875232218 m/s• Delta-V magnitude: 0.651769842549 m/s

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Mid-Term Exam• Problem 3

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Mid-Term Exam• Problem 3

• Use Algorithm 48 again to propagate state of A relative to B. You should see the position go to zero!!!

• The rendezvous Delta-V impulse that A has to perform, in m/s relative to B:

• Delta-Vx: -0.17983714361 m/s• Delta-Vy: -0.066363929565 m/s• Delta-Vz: 0.11873790189 m/s• Delta-V magnitude: 0.225486715161 m/s

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Mid-Term Exam• Problem 3

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Mid-Term Exam• Problem 3

• Answer: yes!

• If satellite A does not do anything, it will collide with the shuttle in about 45 minutes. Half an orbit later.

• If satellite A DOES perform one maneuver, and then no more, it will collide with Satellite B.

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Mid-Term Exam• Problem 4

• Inclination = 90+14 = 104 deg

• Altitude = 1666.18 km

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Big error: sidereal time!

Mid-Term Exam• Problem 5

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Mid-Term Exam• Problem 5

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Mid-Term Exam• Problem 5

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Mid-Term Exam• Problem 5

• mu = muEarth + muMoon = 403503.2405 km3/s2

• rp = 362600 km• ra = 405400 km• a = 384,000 km• e = 0.0557292• Period of lunar orbit: 2353711.295 sec = 39228.5216 min

= 653.80869 hours = 27.242029 days

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Mid-Term Exam• Problem 5

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Mid-Term Exam• Problem 5

• use equation (for example):

• r = 380,000 km + rEarth = 386,378.1363 km

• E = 1.68215420 rad = 96.380336 deg

• Time past periapse: 609395.909 sec = 10156.5985 min = 169.27664 hours = 7.053193 days

• Total Duration within 386378 km: 1218791.818 sec = 20313.1970 min = 338.55328 hours = 14.106387 days

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Mid-Term Exam• Problem 5

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Percentage of time the Earth and Moon are within 386378 km: 51.782%

ASEN 5050SPACEFLIGHT DYNAMICS

A-Train

Prof. Jeffrey S. ParkerUniversity of Colorado – Boulder

Lecture 27: Mid-Term Review, A-Train 40