(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Assuming planar orbits, calculate the Hohmann ∆V required to transfer from a low-Earth

circular orbit with radius of 1.03 Earth radii to the orbit of the Moon (assume 60 Earth

radii). Compare this to the 3-maneuver strategy of (1) escaping to infinity on a parabolic

orbit, (2) maneuvering from infinity to approach the Moon’s radius on a tangential path,

and (3) circularizing at the Moon orbital radius. Use at least 5 significant digits in these

calculations.Locate the crossover point (the ratio r2/r1) where the escape option becomes

more ∆V efficient.

The first parts are solved and cheked to be right.The bold part of the question is the place where i am stuck, finding an iteration to find thecrossover point.

2. Relevant equations

Equations are right, the iteration doesn't work.

3. The attempt at a solution

This is a MATLAB ITERATION.

mu = 3.986004418000000e+005;%gravitaional parameter

r1=1.03*6378;%first point

r2=r1*1.5:1:382680;%final points

for i=1:length(r2);

vesc1=(2*mu/r1)^.5;%escape from leo

vesc2=(2*mu./r2(i)).^.5;%escape from moon

del1=vesc1+vesc2;%left side of deltaone

at=(r1+r2(i))/2;%transfer semimajor axis

et=-mu/2/at;%transfer orbit energy

%%%%%%%%%%%%%%%%%%%%%%%%%

vt1=(2*(et+mu/r1))^.5;%transfer velocity at periapsis1

vt2=(2*(et+mu./r2(i))).^.5;%transfer velocity at apoapsis

v2=(mu./r2(i))^.5;%circular moon orbit velocity

%%%%%%%%%%%%%%%%%%%%%%%%%

del2=vt1-vt2+2*v2;%rhs

del3=del1-del2;%lhs

if del3<0.00001

ratio=r2(i)/r1;%finds the ratio

else

i=i+1;

end

end

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# Homework Help: Orbital Transfer DeltaV Comparison for Different Orbits

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