Computations for FESS 1 Problem Set #2, Problem #2

pset2-2.jl

#!/usr/bin/env julia
################################################################################
# pset2-2.jl 
#
# Josh Kaplan
# _jk@jhu.edu
#
# Computations for Problem Set #2, Problem #2.
################################################################################

#----------( Constants )----------#

R_E = 6378.1        # Radius of Earth   [km]
µ_E = 3.986e5       # µ of Earth        [km^3/s^2] 
K_A = 2.556e8       # For km^2
η = 0
η = η + 10
θ = 10

#----------( Functions )----------#


"""Computes the angular radius of earth in degrees given a radius. 
Source: Space Mission Engineering, Eq. 8-26."""
angular_radius(r) = asind(R_E / r)


"""Computes the elevation angle (in degrees) for a given nadir and radius.
Source: Space Mission Engineering, Eq. 8-28."""
function ε(η, r) 
    frac = sind(η) / (R_E / r)
    
    # Typical satellite geometry
    if 0 <= frac <= 1 
        return acosd(frac)
    # Satellite FOV extends beyond Earth
    elseif frac > 1
        return 0
    else
        println("An error occurred.")
        exit(1)
    end
end

"""Computes lambda max for a given nadir and radius.
Source: Space Mission Engineering, Eq. 8-37."""
λ(η, r) = 90 - η - ε(η, r)

"""Computes the Instantaneous Access Area (IAA) in km^2 given a nadir angle and
radius. Source: Space Mission Engineering. Appendix C, Eq. C-29."""
function IAA(η, r) 
    return K_A * (1 - cosd(λ(η, r)))
end

"""Computes Footprint Area, FA, in km^2. 
Source: SME, Eq. 10-3"""
function FA(η, r) 
    D = R_E * sind(λ(η, r)) / sind(η)   # SME Eq. 8-31
    Wf = D * sind(θ)                    # SME Eq. 10-2b
    elev = ε(η, r)
    if abs(elev) < .001
        Lf = D
    else 
        Lf = D * sind(θ) / sind(elev)    # SME Eq. 10-1b
    end
    return (π/4)*Wf*Lf
end


"""Computes average Area Coverage Rate (ACR_avg) in km^2/s.
Source: SME Eq. 10-5."""
function ACR_avg(η, r)
    DC = 1          # Duty cycle, given
    O_avg = 0.25    # 0.25, given
    T = 1           # 1 sec exposure time, given 
    return DC * (1 - O_avg) * FA(η, r)/T
end


"""Computes Area Access Rate in km^2/s.
Source: SME Eq C-30."""
function AAR(η, r)
    P = 2*π*sqrt(r^3/µ_E)
    return 2*K_A*(sind(λ(η, r))/P)
end

"""Computes the ground speed in km/s."""
function ground_speed(r)
    P = P = 2*π*sqrt(r^3/µ_E)
    return 2*π*R_E / P
end


################################################################################
##                               Problem 1                                    ##
################################################################################

th = "Orbit       IAA           FA        ACR_avg      AAR       Ground Speed\n"
un = "           [km^2]       [km^2]     [km^2/s]     [km/s]         [km/s]  \n"
sp = "-----   -----------   ---------   ----------   --------    ------------\n"
write(STDOUT, "\n")
write(STDOUT, th) # Print table headers
write(STDOUT, un) # Print units
write(STDOUT, sp) # Print separator


##############################
##  Orbit #1 - Planet Labs  ##
##############################
a = R_E + 410           # Semi-major axis (circular)    [km]
i = 51.7                # Inclination                   [deg]
P = 92.77*60            # Period                        [s]
v = 7.663               # Velocity                      [km/s]

# Print results
@printf("#1")
@printf("%15.2f", IAA(η, a))
@printf("%14.2f", FA(η, a))
@printf("%13.2f ", ACR_avg(η, a))
@printf("%9.2f", AAR(η, a))
@printf("%14.2f\n", ground_speed(a))

##############################
###  Orbit #2 - Skybox      ##
##############################
a = R_E + 600           # Semi-major axis (circular)    [km]
i = 97.6                # Inclination                   [deg]
P = 96.69*60            # Period                        [s]       
v = 7.558               # Velocity                      [km/s]

# Print results
@printf("#2")
@printf("%15.2f", IAA(η, a))
@printf("%14.2f", FA(η, a))
@printf("%13.2f ", ACR_avg(η, a))
@printf("%9.2f", AAR(η, a))
@printf("%14.2f\n", ground_speed(a))


###############################
###  Orbit #4 - GEO Telecom  ##
###############################
a = R_E + 35786         # Semi-major axis (circular)    [km]
i = 0                   # Inclination                   [deg]    

# Print results
@printf("#4")
@printf("%15.2f", IAA(η, a))
@printf("%14.2f", FA(η, a))
@printf("%13.2f ", ACR_avg(η, a))
@printf("%9.2f", AAR(η, a))
@printf("%14.2f\n", ground_speed(a))

println("")