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# Monthly Archives: March 2013

## 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]`

## 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```