Planetary Capture

* Türkçesi için

In here, Planetary Capture is considered as capture around smaller body (M2) in CR3BP. Some interplanetary missions require a circularization about the target planet, instead of a soft landing or a flyby. So dynamics of Capture around M2 must be investigated carefully to avoid any unnecessary expensice burn in sake of low-cost. There are actually many types of capture as it is decsribed in Belbruno’s Book [Capture Dynamics and Chaotic Motion in Celestial Mechanics, 2001.]. and In here, I’ll give very simple information about Planetary Capture, for beginner level ^_^.

First of all, captures are clasified in 2 main group;

  • Permanent capture; In its natural dynamics, when a trajectory is bounded around planet (m2) in forward time, but it is unbounded in backward time (or reverse), then it is called Permanent capture. The dynamicly natural permanent capture, which can be captured without any velocity decrement so very adventageous, can be very sensitive and hard to find, esspecially in high energy level (While both L1 and L2 gates are open). But some Permanet capture trajectories can be obtained easily just using and imprisoning them in the zero-velocity-curves (or surface in 3D). Such permanent capture is shown in below. The initial conditions are taken from L1 point, and it is integrated in forward time (Red trajectory, bounded), and backward time (Blue trajectory, unbounded);

  • Temporary capture; In its natural dynamics, when a trajectory is bounded around planet (M2) in specific time span (such as 1 or 2 month, more or less), but then it become unbounded in both forward and backward time, then it is called Temporary capture. This is the most common capture that it can be easily found and obtained in any case and energy level.  The Temporary capture trajectories are also clasified as;
        • Short-term temporary capture, which is bounded in short time span (say less than 1 year) in its natural dynamics.
        • Long-term temporary capture, which is bounded in long time span (say more than 1 year) in its natural dynamics. Note that, very long-term ones (such as more than 5 or 10 years) are actually converge to Permanent capture. This type of capture can be easily found with some map methods, which is explained in my PhD. Thesis. For example, head figure in this post is a long-term temporary capture, which is bounded only about 3.7 years.

In addition, if a velocity decrement (ΔV) is used to make it bounded around M2, then trajectory is turned from temporary to Permanet capture. But it is become an Artificial Permanet capture, of course, because of ΔV. Such as in below plot, a short-term (about 1 month) temporary capture trajectory (Pink) is bounded in various low-altitude circular orbits, with using about ~200-1000 m/sec velocity decrement. This type capture scheme is requried high-cost.

But there are also various low-cost capture scheme, which trajectory is captured in less than 50 m/sec , and bounded in high-altitude nearly-circular parking orbits, such as;

As it is seen in above plots (Earth-Moon binary system), a temporary capture trajectory (left side) can be bounded in very low cost (13 m/s) as shown in right plot; First of all, we choose the initial conditions (i.c) using a mapping method (such as left plot; blue trajectory is coming and red one is leaving, so bonded around Moon (M2) only about ~4 month). Then we desine the capture space mission like that; when trajectory comes in to Moon on the blue trajectory (left plot), we applied a ~13 m/s velocity decrement, which change the energy level, in a certain place (which is found by a map). Then finally, Trajectory is bounded in a very high-altitude nearly circular parking orbits (~7000km), with very low-cost….. How to find this type of low-cost capture trajectories are detaily explained in my thesis detailly, which will be presented later….  but you may ask some questions in advance, if you wish ! ^_^

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