From: spam@merlyn.demon.co.uk   
      
   JRS:  In article <1111494263.223713.54600@g14g2000cwa.googlegroups.com>,   
   dated Tue, 22 Mar 2005 04:24:23, seen in news:sci.space.science,   
   Cray74@gmail.com  posted :   
   >   
   >Monte Davis wrote:   
   >> Dumb question: If one were in circular LEO and crazy enough to want a   
   >> 90-degree change of inclination, what's the cost in delta-v? Is it,   
   >as   
   >> intuition is telling me, equivalent to throwing away all your ~9 kps   
   >> and re-acquiring it all?   
   >   
   >At first glance, a brute force 90-degree plane change would require   
   >1.414x (square root 2 times) as much delta-V as it took to get to   
   >orbit, so 7.8x1.4=11km/s. You have to kill all that horizontal velocity   
   >and replace it with orbital velocity perpendicular to your first.   
      
   But separately they need Root2 times the delta-V of doing them together,   
   and that way one can be less hasty for a given loss of altitude.   
      
   >It would, in fact, be less costly in delta-V to do something like   
   >accelerate to escape velocity (~3.3km/s above orbital velocity), drift   
   >up to about the L1 point or swing around the moon, and drop back to   
   >Earth in a new, desired orbit. I think.   
      
   Let orbital velocity V have magnitude 1.0 units.  Then the right-angle   
   plane change, done be a rapid burn at 45 degrees to original-forwards,   
   needs delta-V of Root2 units, as you say.   
      
   Burns to/from escape velocity needs dV of Root2-1, and plane change is   
   free at infinity.  That dV, applied directly, gives a plane change of   
   2(arcsin(Root2-1) which is about 48.94 degrees,   
      
   Lesser changes than that are better done directly, greater ones better   
   via infinity.  With corrections for practicalities, using lunar gravity,   
   etc.   
      
   OTOH ISTR being corrected on this or a similar matter before; possibly   
   it is better for angles near that to burn to a higher but finite apogee,   
   change plane there, and return.   
      
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