If a planet is in a circular orbit of radius, R, determine the potential energy due to gravity, its kinetic energy due to the motion of the planet, and the total energy. e) A satelite is in geostationary orbit. How much energy is required to move it to a circular orbit where it orbits the Earth once in 8 days?

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Chapter25: Geometric Optics
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a) Show that the torque on a planet orbiting the Sun due to the gravitational attraction of the Sun is zero. b) Show that the area swept out by a planet in time dt is proportional to its angular momentum. c) Using your answers above derive Kepler’s 2nd law. d) If a planet is in a circular orbit of radius, R, determine the potential energy due to gravity, its kinetic energy due to the motion of the planet, and the total energy. e) A satelite is in geostationary orbit. How much energy is required to move it to a circular orbit where it orbits the Earth once in 8 days? You may express your answer in terms of the total energy of the initial geostationary orbit. **Only answer part D and E, answers to previous questions have been provided in the image.**
al
a) de skoay
Jngut or
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• blant abi MisA on
Jorqua n plane t is gimm ad,
t (ixi)
HENCE PROVED
Step2
hị
) o skow that ortn Stat pi l
Pla net ir lime oli preherkor el'
*k ongulor mo mend
dA= r
Ang la lar me me ntum ol ploned L
plavet L
me mentr
my'
mast biouat
L- de
Slep3
dA = 1*de = 1
di
de
dA
Substi luing from ey -) to
get
yL = L
s from ey-) to
a bove ereatie n , ae
dn =
ot
dA = L
dt
2. m
dA L
dt
HENCE PRVED
Step4
d)
c) Ju prove,
epler's seand tu
Il suy dread velesty
Stutimend
is tons tant.
Prual
DA -
1.
JE
-)
teva se el plaut is jeru
Awgunr momerntum is anscaved
L- Cena lant
Ciona font
da : L = rona tent
de
da
- tenalant
HENCE PROVE)
Transcribed Image Text:al a) de skoay Jngut or Clu k Ihe jreui la horai SHotatlian • blant abi MisA on Jorqua n plane t is gimm ad, t (ixi) HENCE PROVED Step2 hị ) o skow that ortn Stat pi l Pla net ir lime oli preherkor el' *k ongulor mo mend dA= r Ang la lar me me ntum ol ploned L plavet L me mentr my' mast biouat L- de Slep3 dA = 1*de = 1 di de dA Substi luing from ey -) to get yL = L s from ey-) to a bove ereatie n , ae dn = ot dA = L dt 2. m dA L dt HENCE PRVED Step4 d) c) Ju prove, epler's seand tu Il suy dread velesty Stutimend is tons tant. Prual DA - 1. JE -) teva se el plaut is jeru Awgunr momerntum is anscaved L- Cena lant Ciona font da : L = rona tent de da - tenalant HENCE PROVE)
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