1L20-001
SpacecraftorbitingMars-orbitalmotion
PROMPTSEMBEDDED
STATEMENTOFTHEPROBLEM
Aspacecraftisorbiting200kmabovethesurfaceoftheplanetMars.Oneoftheastronauts
onboarddropsapen.AtwhatratedoesthepenfallrelativetothesurfaceofMars?How
fastdoesthepenfallrelativetotherestofthespacecraft?
STRATEGY
ThespacecraftisinorbitaboutMars,meaningthatitis
travelinginacircularpath200kmabovethesurfaceof
Mars.Sincetheorbitiscircular,themotionofthe
spacecraft(andeverythingonboarditincludingthepen)
isundergoinguniformcircularmotion;theaccelerationis
thereforeradialacceleration.
Whichdirectionisthespacecraftacceleratingandwhich
objects,ifany,sharethisacceleration?
v
Free-Body
Diagrams
System
a
horbit
Spacecraft
rMars
Fg
Astronaut
Fg
IMPLEMENTATION
Fg
horbit = 200 km
a = ?
rMars = 3,389 km
1.Whatistheorbitalradiusofthespacecraft?
Howistheorbitalradius,thequantity“r”,definedintheequationforuniversalgravitation?
Useyourdefinitiontojustifythatinthisexample𝑟!"#$% = 𝑟!"#$ + ℎ!"#$% .
Whatisthegravitationalforce?
BycombiningthegravitationalforcewithNewton’sSecondLaw,wecanfindthe
accelerationofthespacecraftandeverythingonboard.
WhatistheforceofthespacecraftonMars?WhatistheforceofMarsonthespacecraft?
Pen
1L20-001
SpacecraftorbitingMars-orbitalmotion
PROMPTSEMBEDDED
CALCULATION
1.𝑟!"#$% = 𝑟!"#$ + ℎ!"#$% = 3,389 km + 200 km = 3589 km
2.Combiningthegravitationalforce,𝐹!"#$%&#&%'(#) =
!!!"#$%$&#'( !!"#$
!
!!"#$%
Secondlaw,𝐹!"# = 𝑚𝑎,wefindthemagnitudeofacceleration,𝑎 =
;withNewton’s
!!!"#$
!
!!"#$%
= 3.32
!
!!
.
Theentirespacecraftandeverythinginsideisacceleratingatthesamerate,sothepenwill
notappeartofall.Thepenappearstofloat(beweightless)becausetheastronautobserver
isfallingwithit.
Howdoesthemagnitudeoftheaccelerationduetogravityinorbitcomparetothesurface
valueofaccelerationduetogravityonMars?Howcouldwesolveforthatvalue?Giveitashot
inthespacebelow.Youcan