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) v 0 = 6700 m/s. The equations describing the motion of the smaller spacecraft are:wherer(t) and ?(t) are the polar coordinates of the small spacecraft at a given time.Gis the universal gravitational constant = 6.672*10-11m3/kg-s2andme is the mass of the earth = 5.9742 1024kg. Note thatr(t) =re +h(t), wherere is 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.

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...

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)
v
₀= 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_e
is the mass of the earth = 5.9742 10²⁴kg. Note that
r(t) =
r_e
+
h(t), where
r_e
is 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

Answered Same DayDec 26, 2021

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

David answered on Dec 26 2021

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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.

(a) Convert the above two second-order differential equations to four first-
order...

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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...

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