space invaders science technology engineering ......–measurement –space weather –sun o...
TRANSCRIPT
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
SubjectsandGradeLevels
•Mathematics •Science–Geometry –SunEarthInteractions–Measurement –SpaceWeather
–Sun
o Satellites&Spacecrafts
o GradeLevels7-8,9-10
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
Standards– Science
•DevelopamodelbasedonevidencetoillustratethelifespanoftheSunandtheroleofnuclearfusionintheSun’scoretoreleaseenergythateventuallyreachesEarthintheformofradiation
•CrosscuttingConcepts– Scale,ProportionandQuantity
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
LearningObjectives
•Useunitsofmeasurementandconversionrulestotransformlengthsinastronomicalunits
•Usegeometry,
theLawofSines andtheLawofCosines,formulasforR
todeterminethedistanceandangleofacoronalmassejection
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
SpaceWeatherOverview
•ReferstotheinteractionoftheEarthwiththeSun’satmosphere
•WorkingwithNASADataSatellites/Spacecrafts observingSun
•FeaturesofSpaceWeather
–Sunspots–Flares–CoronalMassEjections
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
All the satellites’spacecrafts!
SolarFlare
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
CoronalMassEjection
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
VanAllenBelts
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
Sun-EarthInfluences
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
Aurora
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
Aurora
SPACE INVADERS Science Technology Engineering &Mathematics
Ma n u e l a PRA JEA H on e y w e l l Edu c a t o r Traian National College
BASICS for Mathematics
-SOLAR STORM Activity-
Astronomical Measurements
A
Ca
c
𝑻𝒉𝒆𝑳𝒂𝒘𝒐𝒇𝑺𝒊𝒏𝒆𝒔
𝒂𝒔𝒊𝒏𝑨 =
𝒃𝒔𝒊𝒏𝑩 =
𝒄𝒔𝒊𝒏𝑪 = 𝟐𝑹
𝑻𝒉𝒆𝑳𝒂𝒘𝒐𝒇𝑪𝒐𝒔𝒊𝒏𝒆𝒔
𝒂𝟐 = 𝒃𝟐 + 𝒄𝟐 − 𝟐𝒃𝒄𝒄𝒐𝒔𝑨
𝑹 =𝒂𝒃𝒄𝟒𝑺
𝑴𝒆𝒈𝒂𝒌𝒊𝒍𝒐𝒎𝒆𝒕𝒆𝒓𝟏𝑴𝒌𝒎 = 𝟏, 𝟎𝟎𝟎, 𝟎𝟎𝟎𝒌𝒎
𝑨𝒔𝒕𝒓𝒐𝒏𝒐𝒎𝒊𝒄𝒂𝒍𝑼𝒏𝒊𝒕𝟏𝑨𝑼 = 𝟏𝟓𝟎𝑴𝒌𝒎
𝑳𝒊𝒈𝒉𝒕𝒀𝒆𝒂𝒓𝟏𝑳𝒀 = 𝟔𝟐, 𝟎𝟎𝟎𝑨𝑼
LAUNCHING THE CHALLENGE!
Mathematical Modeling !
E
A
B
S
C
INFORMATIONS ?
Solving Geometry Problem !
E
A
B
S
C
What dowe assume?What dowe know?Fixthe hypotheses!
Whatdoweknow?
1.TheEarth-SundistanceandthelengthofthetrajectoryofthesatellitepairStereoA&StereoBaroundtheSun(bluecolored)2.WeknowalltheinformationprovidedbythesatellitepairStereoA&StereoBandfromtheEarth:- thedistanceswherethesatellitesarefromEarthandSun(thebluedistances);-theanglesunderwhichthesatellitesseetheCME(C)relativetoEarthandSun(theangleshavingtheverticesinAorB);-theanglebetweenthesatellitesdirectionsseenfromtheEarth.
Whatdoweassume?
1. WeassumethatthetrajectoryofthesatellitesStereoA(StereoAhead)andStereoB(StereoBehind)aroundtheSuniscircular.
2. Weassumethatthetravelspeedsofthesatellitesareconstant.3. WeassumethattheCoronalmassEjectionismovinginstraight
linefromStoCandfromCtoE.4. WeassumethattheEarthandtheSunarenotsignificantly
movingduringtheCoronalMassEjection(C)travels.
What dowe want to find?Fixthe conclusion!
Whatdowewanttofind?
1.ThedistancefromtheCoronalMassEjection(C) totheEarth.2.TheangleunderwhichtheCoronalMassejectionisobservedfromtheEarth(∢𝐶𝐸𝑆).3.ThetimeinwhichtheCoronalMassEjectionwillhittheEarth.
2ways to solve:
Drawing&ScaleapproachUsecompass&rulertomake
scaledrawing
Geometric&Trigonometricapproach
UseLawofsinusandlawofcosinestodeterminethe
distances
TheDrawing&Scaleapproach
Activity:Thestudentswilldrawascalemodeloftheproblemrespectingtheinputsoftheproblematthechosenscale.Withtheprotractortheywilldeterminefirsttheunknownangles(orusingthetheoremreferringatthesumoftheanglesinatriangle).Thentheywillmeasurethelengthoftherequiredsegmentsandusingthescaleofthedrawingtheywilldeterminethelengthoftherequireddistances.
Materialsneeded:compass,protector,ruler,millimeterpaper.
Note:Themeasurementshouldbeasaccurateaspossibleinordertoapproximateabetterresultusingthismethod.Theaccuracyoftheresultiseasytocompromisethinkingthatanerrorof0.1mminthemeasurementcouldleadatsignificantdifferencesthinkingthattheadoptedscaleisverylargebecause1𝑀𝑘𝑚 = 10-𝑘𝑚 = 10.𝑚 = 10/0𝑚𝑚. Byexample, ifthescaleisat1𝑀𝑘𝑚𝑐𝑜𝑟𝑟𝑒𝑠𝑝𝑜𝑛𝑑1𝑐𝑚, thensuchcase0,1𝑚𝑚𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠10, 000𝑘𝑚.
Theinputs/TheOutputs!
Inputs
𝑆𝐴 = 𝑆𝐵 = 𝑆𝐸 = 150𝑀𝐾𝑚Typeequationhere.
𝑚 ∢𝐸𝐴𝑆 = 63V,𝑚 ∢𝐶𝐴𝑆 = 45V𝑚 ∢𝐸𝐵𝑆 = 66V,𝑚 ∢𝐶𝐵𝑆 = 50V
𝑚 ∢𝐴𝑆𝐶 = 68V,𝑚 ∢𝐶𝑆𝐵 = 48,V,𝑚 ∢𝐴𝑆𝐸 = 14V
𝑂𝑢𝑡𝑝𝑢𝑡𝑠
𝐶𝐸 =?𝑚 ∢𝐶𝐸𝑆 =?
HowlongdidittaketotheCoronalMassEjectionlocatedatthismomentinthepointCtohittheEarth,knowingthatitsspeedis2Mkm/hour?
TheGeometric&Trigonometricapproach
TheReasoning Plan!
Findthetimeinwhich
‘C’willhittheEarth!
Thereare2commonunknowninthebothrelations:𝑥 and𝑑.
Eliminate𝑑 betweentherelationsandreachatanequationwithangleshavingtheunknown𝑥.Expandingtheangleaddiction/subtraction
formulasandusinga3-decimaldevicecountingitfindtherelationbetween𝑠𝑖𝑛𝑥and𝑐𝑜𝑠𝑥.
Find𝑥 then𝑑.Findthen𝐵𝐶, 𝐸𝐶, ∢𝐶𝐸𝐵, ∢𝑆𝐸𝐶thenCE.
Denote𝑚 ∢𝐴𝑆𝐶 = 𝑥.Findalltheanglesonthefigure.
Denote𝐶𝑆 = 𝑑.ApplyLawofSinusesinthebothtriangles𝐴𝑆𝐶 and𝐵𝑆𝐶.
Key Answers Sheet
𝑡 = //^_`a0_`a/c
= 58ℎ or2,4𝑑𝑎𝑦𝑠
𝑠𝑖𝑛45sin(315 − 𝑥) =
𝑠𝑖𝑛50sin(208 + 𝑥)
𝑐𝑜𝑠𝑥 = 0,397𝑠𝑖𝑛𝑥,𝑐𝑜𝑠𝑥 = V,/^m/./^m
�, 𝑥 = 68V
𝐶𝑆 = 115, 𝐵𝐶 = 84, 𝐸𝐶 = 47,𝑚 ∢𝑆𝐸𝐶 = 37V
𝑚(∢𝐴𝑆𝐶)= 315 − 𝑥,𝑚 ∢𝐵𝑆𝐶 = 102 − 𝑥,𝑚 ∢𝐵𝐶𝑆 = 208 + 𝑥.opq(∢rst)
u= opq(∢srt
/^V, opq(∢rvt)
u= opq(∢vrt)
/^V.
BibliographyRelatedLinks
https://spacemath.gsfc.nasa.gov/
https://www.nasa.gov/content/goddard/what-is-a-solar-prominence
https://www.nasa.gov/sites/default/files/files/SMIII_Intro_Pages.pdf