Need matlab code and explation of the solution. A large spacecraft orbits the earth at an altitude...

Question

Need matlab code and explation of the solution.

A large spacecraft orbits the earth at an altitude h = 772 km above the surface of the earth. This large spacecraft launches a smaller one with velocity (perpendicular to the earth s surface) v₀= 6700 m/s. The equations describing the motion of the smaller spacecraft are:

where r(t) and ?(t) are the polar coordinates of the small spacecraft at a given time. G is the universal gravitational constant = 6.672*10 ^-11m³/kg-s²and m_eis the mass of the earth = 5.9742 10²⁴kg. Note that r(t) = r_e+ h(t), where r_eis the radius of the earth = 6378:14 km.

1

Convert the above two second-order differential equations to four first-order differential equations. Find the initial conditions. In determining the initial conditions, be careful that units are consistent -1 km = 1000 m. Also recall that angular velocity,
Use the MATLAB function ode45 to integrate the system of ODE s from t = 0 to t = 1200 s. Plot r(t) vs. t and (t) vs. t. Plot r(t) vs. (t) on a polar plot. (This is the spacecraft s trajectory.) What is the value of ? at the time the spacecraft impacts the earth s surface? What is the spacecraft s velocity (both horizontal and vertical directions) when it impacts the earth s surface?
Extra credit. Find the initial velocity that would be required in order that the spacecraft enter a circular orbit. Solve the system of differential equations to show that this velocity will indeed give a circular trajectory. Plot the trajectory. What happens if the initial velocity is 9000 m/s? Plot the trajectory for this case.

005_hlwhazo-mom0kc15.docx

David · Accepted Answer

1. A large spacecraft orbits the earth at an altitude h = 772 km above the 
surface of the earth. This large spacecraft launches a smaller one with 
velocity (perpendicular to the earth s surface) v0 = 6700 m/s. The equations 
describing the motion of the smaller spacecraft are: 
  ̈    ̇  
   
  
 
                                            ̈    
  ̇ ̇
 
  
where r(t) and θ(t) are the polar coordinates of the small spacecraft at a 
given time. G is the universal gravitational constant = 6.672*10 -11 m3/kg-s2 
and me is the mass of the earth = 5.9742 1024 kg. Note that r(t) = re + h(t), 
where re is the radius of the earth = 6378:14 km.

Need matlab code and explation of the solution. A large spacecraft orbits the earth at an altitude h = 772 km above the surface of the earth. This large spacecraft launches a smaller one with velocity...

Solution

Answer To This Question Is Available To Download

Related Questions & Answers

Submit New Assignment