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World Magnetic Model,Matlab

February 12, 2014 4:26 pm / Leave a comment

 

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

April 6, 2013 8:14 am / Leave a comment

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

April 5, 2013 11:03 pm / Leave a comment

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)

April 5, 2013 9:19 pm / Leave a comment

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

March 25, 2013 2:36 pm / Leave a comment

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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