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2016Ph.D.QualifyingFieldExam–SpaceSystems

https://svs.gsfc.nasa.gov/vis/a010000/a011900/a011950/New_Horizons_4Q_poster_v3.png

OnJanuary19,2006,theNewHorizonsspacecraftlaunchedonanAtlasV551rocketfromKennedySpaceCenter,headingtoPluto.ThiswasthefirsttimetheAtlasVwasconfiguredwithfivesolidrocketboostersandthreestages(Centaursecondstage,andATKStar48Bthirdstage).ThevelocityofNewHorizonswithrespecttoEarthafterthethirdstageburnwas16.2km/s.NewHorizonshadclosestapproachtoPlutoonJuly14,2015.

Suggestedassumptions:AssumethattheSun,Earth,Jupiter,Pluto,andspacecraftareallco-planarandincircularorbits.AssumethatthespacecraftdirectionisoutwardawayfromtheSunandtowardPlutoafterEarthlaunch.AssumePlutoisat40AUfromtheSun.AssumeJupiterisat5.2AUfromtheSun.1AU=1.4960×108kmMEarth=5.972×1024kgrEarth=6371kmMSun=1.989×1030kgrSun=6.95700×105kmMJupiter=1.898×1027kgGravitationalconstant:6.67408×10-11m3kg-1s-2

1) WhatΔvisneededtoexittheEarth’ssphereofinfluence?ExplainwhythevelocityofNewHorizonsasitdepartedEarthgiveninthedescriptionabovemaybedifferentthanyouranswer.WhatΔvisneededtoexittheSun’ssphereofinfluencelaunchingfromEarth?

2) WhatistheEarth’sheliocentricvelocity?WhatisJupiter’s?

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Figure1:Spacecraftheliocentricvelocityvs.distancefromtheSun.

3) ExplainFigure1.Howdoesvelocitychangeasafunctionofdistancefromthesun?Expressasamathematicalrelationship,anddescribehowthiscurvewouldbeobtained.

4) Explainhowagravityassistworks.DrawontopofFigure1acurvethatrepresentsthekeyfeaturesofaJupitergravityassistwithanincreaseinheliocentricvelocityof5km/s.Explainhowtherelationshipbetweenturningangleandaltitudeofperiapseatclosestapproachaffectstheoutcomeofthegravityassist.

5) HowlongwouldittakeNewHorizonstoarriveatPluto’sorbitwithoutagravityassist,usingaHohmanntransferfromEarth’sorbittoPluto’s?

6) ExplainwhyitmaybeunwiseforaspacecraftsuchasNewHorizonstoflybyEarth.

7) DescribeadditionalsystemsdesignsimportanttoaddressforamissionfarbeyondPluto,liketothehypothesized9thplanetortheSolarGravityLensFocus(550AU).

http://news.discovery.com/space/using-the-sun-as-a-magnifying-glass.htm

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45Spacecraft Velocity vs. Distance