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# Category Archives: Spacecraft-Environment Interactions

## Escape velocity,Sun and Earth surface

In this example we calculate the acceleration of gravity and the escape velocity at the Sun and Earth surface.

clc;clear all; G = 6.67384E-11; %Gravitational constant,[m^3kg-1s-2]

## Sun

Ms = 1.98855e30; %Solar mass [kg] Rs = 6.955e8; %Solar radius [m] V_esc = (2*G*Ms/Rs)^0.5/1000; %Escape velocity [km/s] g = G*Ms/Rs^2; %Acceleration of gravity[m*s-2] fprintf('Acceleration of gravity[m*s-2] %4.2f \n',g); fprintf('Escape velocity [km/s] %4.2f \n\n',V_esc);

Acceleration of gravity[m*s-2] 274.36 Escape velocity [km/s] 617.76

## Earth

Me = 5.98e24; %Earth mass [kg] Re = 6378000; %Earth radius [m] V_esc = (2*G*Me/Re)^0.5/1000; %[km/s] g = G*Me/Re^2; %Acceleration of gravity[m*s-2] fprintf('Acceleration of gravity[m*s-2] %4.2f \n',g); fprintf('Escape velocity [km/s] %4.2f \n',V_esc);%% Earth

Acceleration of gravity[m*s-2] 9.81 Escape velocity [km/s] 11.19

## Impact probability,Leonid storm

Calculate the impact probability during a major Leonid storm which has a meteor flux of 8.63e-8 m-2s-1 and lasts for t hours. Do the probability analysis for a GEO spacecraft of size A m^2. What would the risk be during a normal Leonid storm, flux 4.69e-11 m-2s-1?

clc; clear all; N = [1 2 3 4 5 6 7]; %Number of impacts t = 2.5*3600; %[s] Fm = 8.63e-8; %Major Leonid storm meteor flux m-2s-1 Fn = 4.69e-11; %Normal Leonid storm meteor flux m-2s-1 A = 20; %m^2

## Probability of N impact

Major

```
Pm = (Fm*A*t).^N*exp(-Fm*A*t)./factorial(N);
Pmt= sum(Pm);
fprintf('Probability of impact %4.2d \n',Pmt);
```

Probability of impact 1.54e-002

Normal

```
Pn = (Fn*A*t).^N*exp(-Fn*A*t)./factorial(N);
Pnt= sum(Pn);
fprintf('Probability of impact %4.2d \n',Pnt);
```

Probability of impact 8.44e-006

figure(1); semilogy(N,Pm,'r*') hold on; semilogy(N,Pn,'.') xlabel('Number of impacts'); ylabel('Probability of N impact'); title('Impact probability,Leonid storm'); legend('Major','Normal');