Ballistic Skip Capture fact or fiction?

The concept presented here is pretty simple but I am not a trajectory design guy so if I misunderstand something or misstate something please don’t jump all over me.

I understand the Traditional L1 Ballistic capture issue as follows,  In order to get to the moon a velocity on the order of ~3.2 km/s is needed but the moon travels at 1km/s and can only hold onto spacecraft practically at an additional velocity of ~1 km/s.  So there needs to be a large burn to slow down at the moon.  So the total energy to moon orbit is around 4500 to 5500 m/s.

Traditional ballistic capture partially solves this problem by going to L1 and losing kinetic energy in a way I don’t fully understand.  The result of this maneuver is to reduce the delta v by 25%  to 3500-4000 m/s.

My concept is to use a different maneuver or set of maneuvers to achieve a higher percentage or faster maneuver time.  I call this Ballistic Skip Capture.  The concept is relatively simple.  First imagine a spacecraft that is too fast to orbit the moon but to slow to escape the earth.  It starts on the lunar plane as opposed to the equatorial plane and it is rotating in the same direction as the moon but starts behind and at a greater radius than the moon.

 

See image 1

ballistic skip capture1

 

in .pdf form below

ballistic skip capture1

The spacecraft enters the lunar sphere of influence as it aims towards earth and enters a hyperbolic orbit around the moon as it travels between the moon and the earth it speeds up to pass the moon as it is deflected.  It exits this hyperbolic orbit aimed roughly towards deep space but with a radial velocity circling earth that is now slower than the moon but with a normal velocity that makes up the remaining energy.  But the spacecraft is slightly ahead of the moon in terms of angular position on the lunar plane.  The spacecraft escapes the lunar sphere of influence and enters into the earth- lunar gravity and a parabolic orbit to return it to the earth.  While it is out of the way the moon passes it in terms of rotating around the earth.

The angle of the craft and velocity are precisely what is needed to return to the lunar radius orbit such that the spacecraft will again enter into a hyperbolic orbit with the moon from outside and behind.

ballistic skip capture2

The velocity loss mechanism is gravity slingshot that occurs as the spacecraft passes the moon.  If a spacecraft is bent around a moving body such that at the end it is more closely aligned in velocity direction with the moving body then the spacecraft total velocity will increase.  If the spacecraft is bend around a moving body such that it is less aligned with the motion of the moving body then the spacecraft total velocity is decreased.

After the first interaction aka skip the spacecraft seems at first glance  to not be able to lose velocity because it is moving from nearly perfectly aligned with the lunar rotation vector towards a vector that is more pointed into deep space.

The second interaction is limited in that it should be impossible to lose more velocity if the radial rotation speed is fixed and cannot be misaligned.  However the fact that the moon is rotating around the earth and not in a straight line seems to me to make the parabolic arc non symmetrical.  A velocity outward to deep space is bent back towards the earth but because the moon has moved in an arc the slope of the parabola at the time it intersects the moon hyperbolic segment again is more closely aligned to the moons velocity and hence has a small amount of energy that can be transferred to the moons momentum each “skip”

The tools to properly model this are not at my disposal so I am currently in a state of not being sure that what appears to me to be a workable idea is actually workable or not.  Another possibility is that small burns can be magnified by the slingshot effect for a fast capture.  The final insertion orbit would likely still involve a burn and its very possible that this method even if it works is not as attractive as Traditional L1 Ballistic Capture but I think its an interesting exercise to model even if it turns out to not be a useful idea.

The exorcise of building a lunar half orbit seems to me to have some artistic merit even if there is no engineering or physics merit.

An advantage to Ballistic Skip Capture is that if this approach works it should work for every planet in the solar system even though there may not be a convenient L1 at the correct energy potential for Mars or Venus etc.

 

Thank you for your time,

Darrin

 

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