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World Magnetic Model,Matlab

 

close all;clear all;clc;
height = 500000; % A scalar value, in meters
lat = -90:2.5:90;  % geodetic latitude, in degrees, where north latitude is
%positive, and south latitude is negative
lon = -180:2.5:180;  % geodetic longitude, in degrees,
%where east longitude is positive,and west longitude is negative
% dyearA scalar decimal year. Decimal year is the desired year in
%a decimal format to include any fraction of the year that has already passed.
sla = size(lat);
sln = size(lon);
for i = 1:sla(2)
    for j =1:sln(2)
        [Bxyz, h, dec, dip, f] = ...
        wrldmagm(height, lat(i), lon(j), decyear(2014,1,22),'2010');
    % Note that WMM-2010 isvalid from January 1, 2010, until December 31,
    % 2014
    % Bxyz Magnetic field vector in nanotesla (nT)
    % h Horizontal intensity in nanotesla (nT)
    % dec Declination in degrees
    % dip Inclination in degrees
    % f Total intensity in nanotesla (nT)
        Bx(i,j) = Bxyz(1,1);
        By(i,j) = Bxyz(2,1);
        Bz(i,j) = Bxyz(3,1);
        Bm(i,j) = f;
%          [Bxyz(i,j), h(i,j), dec(i,j), dip(i,j), f(i,j)] = ...
%             wrldmagm(height, lat(i), lon(j), decyear(2014,1,22),'2010');
    end
end

Z component

xwidth = 640;
ywidth = 320;
colormap jet
hFig = figure(1);
contourf(lon,lat,Bz)
hold on
set(gcf,'PaperPositionMode','auto')
set(hFig, 'Position', [100 100 xwidth ywidth])
axis([-180 180 -90 90])
colorbar
load('topo.mat','topo','topomap1')
contour(0:179,-90:89,topo(:,1:180),[0 0],'.k')
contour(-180:-1,-90:89,topo(:,181:360),[0 0],'.k')
ylabel('Latitude [deg]')
xlabel('Longitude [deg]')
title('World Magnetic Model, Bz(nT) at Alt = 500 km')

MagneticField_01

Component X

hFig = figure(2);
contourf(lon,lat,Bx)
hold on
set(gcf,'PaperPositionMode','auto')
set(hFig, 'Position', [100 100 xwidth ywidth])
axis([-180 180 -90 90])
colorbar
load('topo.mat','topo','topomap1')
contour(0:179,-90:89,topo(:,1:180),[0 0],'.k')
contour(-180:-1,-90:89,topo(:,181:360),[0 0],'.k')
ylabel('Latitude [deg]')
xlabel('Longitude [deg]')
title('World Magnetic Model, Bx(nT) at Alt = 500 km')

MagneticField_02

Component Y

hFig = figure(3);
contourf(lon,lat,By)
hold on
set(gcf,'PaperPositionMode','auto')
set(hFig, 'Position', [100 100 xwidth ywidth])
axis([-180 180 -90 90])
colorbar
load('topo.mat','topo','topomap1')
contour(0:179,-90:89,topo(:,1:180),[0 0],'.k')
contour(-180:-1,-90:89,topo(:,181:360),[0 0],'.k')
ylabel('Latitude [deg]')
xlabel('Longitude [deg]')
title('World Magnetic Model, By(nT) at Alt = 500 km')

MagneticField_03

Total intensity in nanotesla (nT)

hFig = figure(4);
contourf(lon,lat,Bm)
hold on
set(gcf,'PaperPositionMode','auto')
set(hFig, 'Position', [100 100 xwidth ywidth])
axis([-180 180 -90 90])
colorbar
load('topo.mat','topo','topomap1')
contour(0:179,-90:89,topo(:,1:180),[0 0],'.k')
contour(-180:-1,-90:89,topo(:,181:360),[0 0],'.k')
ylabel('Latitude [deg]')
xlabel('Longitude [deg]')
title('World Magnetic Model, Total intensity(nT) at Alt = 500 km')

MagneticField_04

Spacecraft shielding

For a particle traveling at V km/s, how thick should the shielding be to prevent the meteoroid from penetrating? Assume the meteoroid, having a density of 3.5 g/cm3 and mass of 1e-3 g, impacting into aluminum. The material constant for aluminum is 0.351.

clc;clear all;
Vm = 17:2:71;        %Particle speed range [km/s]
ro = 3.5;            %Particle density [g/cm^3]
m  = 1e-3;           %Particle mass [g]
C = 0.351;           %Material constant for aluminum
ts = C*ro^(1/6)*m^0.352*Vm.^0.857;  %Shielding thickness[cm]
plot(Vm,ts);
hold on;grid on;
plot(Vm,ts,'*');
xlabel('Particle speed [km/s]');
ylabel('Shielding thickness [cm]');
title('Shielding thickness vs particle(mass 1^-^3g) speed');

Shielding

Sputtering, Impact threshold energy

In this example we estimate the fraction of oxygen atoms in the atmosphere at 350 km altitude that have sufficient energy to induce sputtering on Ag and Al. Assume a Maxwellian distribution of oxygen. In order for sputtering to occur, the impact energy must exceed a threshold which is proportional to the binding energy of a surface atom to its neighbors  Assume the binding energy U of a surface atom is 48 eV for Ag and 3.4 eV for Al.

clc;clear all;

% Given:
% Atomic Mass
M_Al = 26.98;           %[amu]
M_Ag = 107.87;          %[amu]
M_O  = 16;              %[amu]
amu  = 1.66053892e-27;  %[kg]
ev   = 1.60217657e-19;  %[J]
mu   = 398600;          %Standard gravitational parameter [km^3s-2]
kb   = 1.3806488e-23;   %[JK-1] Boltzmann constant
Re   = 6378;            %Earth Radius[km]
Alt  = 350;             %[km]
T    = 900;             %[K]
% Binding energy U of a surface atom
U_Al = 3.4;
U_Ag = 48;

Because M_O/M_Al > 0.3 for impacting O of mass mi on a target Al atom of mass mt the energy threshold Eth to induce sputtering is

E_th_Al = 8 *U_Al*(M_O/M_Al)^0.4;
fprintf('Energy threshold of oxygen atoms to induce sputtering on Al Eth = %4.2f eV\n',E_th_Al);
Energy threshold of oxygen atoms to induce sputtering on Al Eth = 22.07 eV

Because M_O/M_Ag <= 0.3 for impacting O of mass mi on a target Ag atom of mass mt the energy threshold Eth to induce sputtering is

gamma= 4*M_O*M_Ag/(M_O+M_Ag)^2;
E_th_Ag = U_Ag/gamma/(1 - gamma);
fprintf('Energy threshold of oxygen atoms to induce sputtering on Ag Eth = %4.2f eV\n',E_th_Ag);
% In order to sputtering to occur, the impacting atom need to have a 1D
% velocity such that
V_Al = (2*E_th_Al*ev/(M_O*amu))^0.5/1000;   %[km/s]
V_Ag = (2*E_th_Ag*ev/(M_O*amu))^0.5/1000;   %[km/s]
% Spacecraft velocity around Earth
V_sc = (mu/(Re + Alt))^0.5;
% Minimum impact velocity relative to spacecraft
V_Alr = V_Al - V_sc     %[km/s]
V_Agr = V_Ag - V_sc
Energy threshold of oxygen atoms to induce sputtering on Ag Eth = 193.94 eV

V_Alr =

    8.6179

V_Agr =

   40.6672

Fraction of O that will induce sputtering on Al belongs to an interval [f_min, f_max]

x = (M_O*amu/(kb*T))^0.5*V_Alr*1000;
f_min = 1/(2*pi)^0.5*exp(-x^2/2)*(1/x - 1/x^3);
f_max = 1/(2*pi)^0.5*exp(-x^2/2)*1/x;
fprintf('%4.3d < Oxygen fraction that will induce sputtering on Al < %4.3d \n',f_min, f_max)
1.036e-036 < Oxygen fraction that will induce sputtering on Al < 1.042e-036

Fraction of O that will induce sputtering on Ag belongs to an interval [f_min, f_max]

x = (M_O*amu/(kb*T))^0.5*V_Agr*1000;
f_min = 1/(2*pi)^0.5*exp(-x^2/2)*(1/x - 1/x^3);
f_max = 1/(2*pi)^0.5*exp(-x^2/2)*1/x ;
fprintf('%4.3d < Oxygen fraction that will induce sputtering on Ag < %4.3d \n',f_min, f_max)
 000 < Oxygen fraction that will induce sputtering on Ag <  000

 

Amount of Out-Gassed Mass due to Diffusion,Total Mass Loss (TML)

Calculate the amount of mass that will be out-gassed each day during the first week on orbit by a 10 kg source with Ea = 10 kcal/mole that meets the ASTM E 595 requirements and is held at a temperature T. The ASTM E595 requirement is that a surface at T = 125 C and a pressure less than 7e-3 Pa during 24 hours should have a Total Mass Loss (TML) less than 1%. Given:

clc; clear all;
Ea = 10;            % Ea is the activation energy [kcal/mole]
R  = 1.9859e-3;     % R is the gas constant [kcal mole-1 K-1]
M  = 12;            % Source Mase [kg]
Days = 7;           % Out-gassing interval [day]
dm = 0.01*M;                  % Allowed Total Mass Loss[kg]
Ts  = 125 + 273.15 ;          % [K]
% q0 - describes the specific out-gassing characteristics of the material
q0 = dm/(2*exp(-Ea/(R*Ts)));  % [kg/day^0.5]

Find the amount of mass out-gassed between time t1 and t2

T = [0,25,50,75,100,125];
dm = zeros(7,6);
fprintf('Amount of mass out-gassed each day during a week, M_i = 12kg\n\n');
fprintf('Day  %4d   %4d    %4d     %4d     %4d     %4d [C] \n',T);
T = T + 273.15; % [K]
for i = 1:Days
    dm(i,:) = q0*(2*exp(-Ea./(R*T)))*(i^0.5-(i -1)^0.5)*1e3; %[g]
   fprintf([num2str(i),'     %4.3f  %4.3f   %4.3f   %4.3f   %4.3f    %4.3f \n'],(dm(i,:)));
end
Amount of mass out-gassed each day during a week, M_i = 12kg

Day     0     25      50       75      100      125 [C] 
1     0.368  1.726   6.374   19.514   51.427    120.000 
2     0.152  0.715   2.640   8.083   21.302    49.706 
3     0.117  0.548   2.026   6.202   16.345    38.140 
4     0.099  0.462   1.708   5.229   13.780    32.154 
5     0.087  0.407   1.505   4.607   12.140    28.328 
6     0.078  0.368   1.360   4.165   10.976    25.611 
7     0.072  0.339   1.251   3.830   10.093    23.551
figure(1);
semilogy(dm);
hold on;
semilogy(dm,'*');
title('Amount of mass out-gassed each day during a week, M_i = 12kg');
legend('0 C^o','25 C^o','50 C^o','75 C^o','100 C^o','125 C^o');
xlabel('Days');
ylabel('Out-gassed mass[g]');

Out_gassed_mass

 

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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