Archive for the ladee Category

Flying moondust

Posted in ladee, moon on January 20, 2011 by moonmapper

Contrary to what was said in the previous post, our Moon does have an atmosphere… sort of.

When orbiting an airless body, one would expect no light scattering to occur. But when the Apollo astronauts were doing circles above the lunar surface, when approaching the terminator they saw this:

"Twilight rays" as sketched by the Apollo 17 crew. Click to enlarge.

What was that?

Dust.

Universe Today has a story on this, which quotes a scientist investigating this phenomenon:

“For the first set of experiments, imagine just a piece of surface with dust particles on it, and we shine light on this surface,” he said, “so that half is illuminated, half is not, pretending that there is a terminator region, that the sun is set on one side and is still shining light on the other. When you shine light on the surface with properties that are appropriate, you can emit photo electrons, but you only emit electrons from the lit side, and some of those electrons land on the dark side, — you have a positive charge surplus on the lit and a negative charge pile-up on the night side. Across a couple of millimeters you can easily generate a potential difference of maybe a watt volt, or a handful of watts volts, which translates actually as a small-scale, but incredibly strong electric fields. This could be like a kilowatt kilovolt over a meter. But of course, it only exists over a sharp boundary, and that sharp boundary may be the key to understanding how you get dust moving to begin with.”

(I took liberty of fixing obviously mistaken physical units).

Okay. Since someone has already done the hard part (i.e. calculated electric field near the lunar terminator), we can now apply high school physics, to calculate how fast can dust be ejected from the terminator zone. The result is below (click to enlarge).

Electrostatic acceleration of dust particles on lunar surface (V=1V, s=1mm)

Electrostatic acceleration of dust particles on lunar surface (V=1kV, s=1m)

The analysis assumes that a constant electric field exists across the lunar terminator. The first graph assumes that the acceleration happens  with the potential difference of V=1V along the distance of s=1mm. The second graph assumes a potential difference of V=1000V along the distance of s=1m. In both cases the electric field is 1kV/m (see the quote above), but the result is not the same. Since it’s known that the potential difference between the light and dark side of the Moon is several hundred volts, then probably the second version is closer to the truth.

Dust grains made of different elements are investigated. For each element, two curves are plotted. The bottom one assumes that only a single atom in the grain has been ionized once (i.e. the electric charge of the grain is equal to the elementary charge). The top one assumes that 50% of surface atoms have been ionized once (the illuminated side of the grain becomes ionized).

Please be aware, that this calculation is based on some highly speculative assumptions. The model is highly sensitive to the parameters of electric field near the lunar terminator.

I hope we will know more on this fascinating subject when LADEE flies.

Related:

MATLAB/Octave code is below.

function moondust()
A_Au = 197;     rho_Au = 19300;
A_Al = 27;      rho_Al = 2700;
A_Fe = 55.8;    rho_Fe = 7874;
A_Ca = 40;      rho_Ca = 1550;

figure;

plot_speed(A_Au, rho_Au, 'y;Au;');
plot_speed(A_Al, rho_Al, 'k;Al;');
plot_speed(A_Fe, rho_Fe, 'b;Fe;');
plot_speed(A_Ca, rho_Ca, 'g;Ca;');

print dust_velocity.png;
endfunction

function v = dust_velocity(q, m)

% V and s estimates from: http://www.universetoday.com/81727/lunar-dust-transport-still-a-mystery/#more-81727

V = 1; % Volts
s = 1e-3; % meters

E = V/s;
a = q/m*E;

t = sqrt(2*s /a);

v = a*t;

endfunction

function plot_speed(A, rho, style)

amu = 1.66e-27;  % atomic mass unit [kg]
q = 1.6e-19;     % elementary charge [C]
%A = 197;        % atomic mass (Au)
%rho = 19300;    % density (Au) [kg/m^3]
v_esc = 2380;    % escape velocity [m/s]

NN = logspace(0, 10, 100);  % number of atoms in the grain

vv1 = [];
vv2 = [];

mm = A*amu*NN;
for N=NN
 m = A*amu*N;

 % Worst case: single atom in the grain ionized
 vv1 = [vv1; dust_velocity(q, m) ];

 % Best case: half of grain surface completely ionized
 qx = N^(2/3)/2;
 qx = floor(qx);
 if qx == 0
 v = nan();
 else
 v = dust_velocity(qx*q, m);
 end
 vv2 = [vv2; v ];
end

% calculate grain size [nm]
grain = (mm/rho).^(1/3) / 1e-9;

if ishold()
else
loglog(grain, v_esc*ones(1, length(grain)), 'r;escape velocity;');
end

hold on;
loglog(grain, vv1, style);
loglog(grain, vv2, style(1));

xlabel('grain size [nm]');
ylabel('velocity [m/s]');
title('Electrostatic transport of particles on lunar surface');
endfunction

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