Introduction to Space Communications PHYS 3250 3.0
Midterm Exam Information
Hand calculators are permitted, but written notes, books and computers are not.
Questions will be taken from all the material covered in class, the assignments and the
handouts.
Some basic equations and constants as given below have to be known and will not be
provided during the exam.
The meaning of the following variables and constants is as discussed in class.
Equations:
1. ν = ν 0 (1± v /c) Doppler effect. Note: v is velocity
2. M = n(t − t p )
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3. Kepler’s first and second laws
2
4. P0 =
5. λ =
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Mean anomaly at epoch t after passing the perigee at time tp
4π 2 3
a
GM
c
ν
Constants:
1.
2.
3.
4.
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5.
Kepler’s third law in the Newtonian version
Wavelength-frequency relation. Note: ν is frequency
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c= 3 • 108 m/s
Earth’s orbital period: 366.2422 mean sidereal days = 365.2422 mean solar days
Mean sidereal day = 365.2422 / 366.2422 mean solar day
Inclination of Earth’s orbital plane with respect to equatorial plane = 23.4 deg
Mean solar constant, E0= 1.37 kW/m2 with an annual variation about the mean of 0.05 kW/m2
Information page attached to the midterm exam
GENERAL EQUATIONS AND CONSTANTS
(may or may not be needed)
Equations:
1.
Polar equation of the ellipse. Note: ν is the true anomaly
2
r=
a(1− e )
1+ ecosν
2
e=
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a −b
a2
2
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2. R⊕ = RE [1-(sin2 λE) I 298.257]
3. Az: azimuth of satellite
tg A = - (tg |B|) / sin λE
B = ΦE - ΦS
λE < 0; B < 0 : Az = A
λE < 0; B > 0 : Az = 360o – A
λE > 0; B < 0 : Az = 180o + A
λE > 0; B > 0 : Az = 180o – A
4. ρ : range of satellite
ρ := [R⊕2 + (RE + h)2 - 2R⊕(RE + h) cos c]1/2
cos c = cos λE cos B
5. El : elevation of satellite
cos El = [(RE + h) / ρ] sin c
Constants:
RE = 6378.0 km
GM = 3.98605 ⋅ 1014 m3 s-2