ISS Eclipse Determination

Determining how much sunlight a body is receiving.

Determining the eclipses a satellite will encounter is a major driving factor when designing a mission in space. Thermal and power budgets have to be made with the fact that a satellite will periodically be in the complete darkness of space with no solar radiation to power the solar panels and keep the spacecraft from freezing.

What is an Eclipse

Geometry of an Eclipse

Body Radius’s and Position Vectors

The Code

Show code

using Unitful
using LinearAlgebra
using SatelliteToolbox
using Plots
using Colors
theme(:ggplot2)

ISS = tle"""
ISS (ZARYA)
1 25544U 98067A   21103.84943184  .00000176  00000-0  11381-4 0  9990
2 25544  51.6434 300.9481 0002858 223.8443 263.8789 15.48881793278621
"""

orbit = init_orbit_propagator(Val(:twobody), ISS[1]);
time = 0:0.1:((24 / ISS[1].n) .* 60 * 60);
o, r, v = propagate!(orbit, time);

function sunlight(Rbody, r_sun_body, r_body_sc)
    Rsun = 695_700u"km"
    
    hu = Rbody * norm(r_sun_body) / (Rsun - Rbody)
    
    θe = acos((r_sun_body ⋅ r_body_sc) / (norm(r_sun_body) * norm(r_body_sc)))

    θu = atan(Rbody / hu)
    du = hu * sin(θu) / sin(θe + θu)

    θp = π - atan(norm(r_sun_body) / (Rsun + Rbody))
    dp = Rbody * sin(θp) / cos(θe - θp)

    S = 1
    if (θe < π / 2) && (norm(r_body_sc) < du)
        S = 0
    end
    if (θe < π / 2) && ((du < norm(r_body_sc)) && (norm(r_body_sc) < dp))
        S = (norm(r_body_sc .|> u"km") - du) / (dp - du) |> ustrip
    end

    return S
end

S = r .|> R -> sunlight(6371u"km", [0.5370, 1.2606, 0.5466] .* 1e8u"km", R .* u"m")

Plotting the Results

Show code

light_range = range(colorant"black", stop = colorant"yellow", length = 101);
light_colors = [light_range[unique(round(Int, 1 + s * 100))][1] for s in S];

plot(
    LinRange(0, 24, length(S)),
    S .* 100,
    linewidth = 5,
    legend = false,
    color = light_colors,
);

xlabel!("Time (hr)");
ylabel!("Sunlight (%)");
title!("ISS Sunlight Over a Day")

Figure 1: Rocket Motor Data: [@thrustcurve]