## Brightness of the spacecraft Glow

In LEO orbits, the interaction of the spacecraft surfaces with the ambient molecules leads to phenomen known as glow. It creates a light contamination in some areas of the spacecraft which is a problem for missions with optical instruments. Glow creates a noice on the measured signal.

clear all;clc; h = 200; %[km] Altitude, Circular orbit % The brightness of the glow B = 10^(7 - 0.0129*h); %[Rayleigh] fprintf('The brightness of the glow %4.2f [Rayleigh]\n',B);

The brightness of the glow 26302.68 [Rayleigh]

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## Debye length, plasma frequency and cyclotron frequency

The calculation of characteristic Debye length, plasma frequency and cyclotron frequency of electrons in the ionosphere, the plasmasphere, the outer magnetosphere and the solar wind.

clc;clear all; me = 9.109E-31; %[kg] Electron rest mass mp = 1.673E-27; %[kg] Proton rest mass eps0 = 8.8542E-12; %[A*s/(V*m)] Permittivity e = 1.602E-19; %[C] Elementary charge Re = 6.37E6; %[m] Earth’s radius Md = 8E15; %[T*m3] Earth’s magnetic dipole moment

## Ionosphere

n = 1E12; %[m-3] Electron density kTe = 0.1; %[eV] Thermal energy r = Re + 3E5; %[km] Radial distance from the Earth’s center wp = (e^2*n/(eps0*me))^0.5/(2*pi); %[Hz] Plasma frequency lD = (eps0*kTe/(n*e))^0.5; %[m] Debye length B = 2*Md/r^3; %[T] Earth’s magnetic field Fc = e*B/(2*pi*me); %[Hz] Cyclotron frequency fprintf('Debye length %4.2d [m]\n',lD); fprintf('Plasma frequency %4.2d [Hz]\n',wp); fprintf('Cyclotron frequency %4.2d [Hz]\n\n',Fc);

Debye length 2.35e-003 [m] Plasma frequency 8.98e+006 [Hz] Cyclotron frequency 1.51e+006 [Hz]

## Plasmasphere

n = 1E7; %[m-3] Electron density kTe = 1; %[eV] Thermal energy r = 5*Re; %[km] Radial distance from the Earth’s center wp = (e^2*n/(eps0*me))^0.5/(2*pi); %[Hz] Plasma frequency lD = (eps0*kTe/(n*e))^0.5; %[m] Debye length B = 2*Md/r^3; %[T] Earth’s magnetic field Fc = e*B/(2*pi*me); %[Hz] Cyclotron frequency fprintf('Debye length %4.2d [m]\n',lD); fprintf('Plasma frequency %4.2d [Hz]\n',wp); fprintf('Cyclotron frequency %4.2d [Hz]\n\n',Fc);

Debye length 2.35e+000 [m] Plasma frequency 2.84e+004 [Hz] Cyclotron frequency 1.39e+004 [Hz]

## Outer magnetosphere

n = 1E6; %[m-3] Electron density kTe = 50; %[eV] Thermal energy r = 7*Re; %[km] Radial distance from the Earth’s center wp = (e^2*n/(eps0*me))^0.5/(2*pi); %[Hz] Plasma frequency lD = (eps0*kTe/(n*e))^0.5; %[m] Debye length B = 2*Md/r^3; %[T] Earth’s magnetic field Fc = e*B/(2*pi*me); %[Hz] Cyclotron frequency fprintf('Debye length %4.2d [m]\n',lD); fprintf('Plasma frequency %4.2d [Hz]\n',wp); fprintf('Cyclotron frequency %4.2d [Hz]\n\n',Fc);

Debye length 5.26e+001 [m] Plasma frequency 8.98e+003 [Hz] Cyclotron frequency 5.05e+003 [Hz]

## Solar wind

n = 1E6; %[m-3] Electron density kTe = 5; %[eV] Thermal energy wp = (e^2*n/(eps0*me))^0.5/(2*pi); %[Hz] Plasma frequency lD = (eps0*kTe/(n*e))^0.5; %[m] Debye length B = 1E-8; %[T] Earth’s magnetic field Fc = e*B/(2*pi*me); %[Hz] Cyclotron frequency fprintf('Debye length %4.2d [m]\n',lD); fprintf('Plasma frequency %4.2d [Hz]\n',wp); fprintf('Cyclotron frequency %4.2d [Hz]\n\n',Fc);

Debye length 1.66e+001 [m] Plasma frequency 8.98e+003 [Hz] Cyclotron frequency 2.80e+002 [Hz]

## Fundamental constants

c = 2.9979E8; %[m/s] Speed of light mu0 = 4*pi*1E-7; %[V*s/(A*m)] Permeability eps0 = 8.8542E-12; %[A*s/(V*m)] Permittivity G = 6.672E11; %[N*m2/kg2] Gravitation constant me = 9.109E-31; %[kg] Electron rest mass mp = 1.673E-27; %[kg] Proton rest mass e = 1.602E-19; %[C] Elementary charge k = 1.381E-23; %[J/K] Boltzmann constant h = 6.626E-34; %[J*s] Planck’s constant Me = 5.98E24; %[kg] Earth’s mass Re = 6.37E6; %[m] Earth’s radius Ms = 1.989E30; %[kg] Solar mass Rs = 6.966E8; %[m] Solar radius Md = 8E15; %[T*m3] Earth’s magnetic dipole moment R = 1.985E-3; %[kcal/(mole*K)]Gas constant