Phase II Final Report - NASA's Institute for Advanced Concepts

Chapter 3.0 Vehicle Design
3.6 Power System
The latitude (φ) and Earth's declination angle (δ) vary with the day of the year (d). This day
number (d) is based on the vernal equinox.
δ = δ max sin(2 π d / d t ) Equation 3-64
The hour angle (a) is given by the following expression, where i is the instantaneous time of day
in hours.
a = 2 π i / h l Equation 3-65
SI o = SI om ( r m 2 / r 2 ) Equation 3-66
The distance from the flight planet to the sun (r) varies throughout the year. The planet's orbital
radius is based on the mean radius (r m ) and is represented by Equations 3-67 and 3-68, where the
day number (d p ) is based on the date of perihelion.
r = r m (1 - e 2 ) / (1 + e cos(θ)) Equation 3-67
θ = 2 π d p / d t
Equation 3-68
Based on the equations given above, power-available curves were generated. The curves represent
the available power at different times of the year and different latitudes. Four times of year
were plotted: vernal equinox, summer solstice, autumnal equinox, and winter solstice. These
dates represent the maximum and minimum points for the year as well as the times of equal day
and night cycle lengths. Figures 3-173 through 3-177 show the power available on Mars.
60
0° Latitude
50
40
Vernal Equinox (Day 1)
Summer Solsitce (Day 167)
Autimal Equinox (Day 333)
Winter Solstice (Day 500)
30
20
10
0
0 5 10 15 20
Time (hours)
Figure 3-173: Mars: Available Power Throughout the Day at 0 o Latitude
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