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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');```