Today I was puzzled when my son was holding a school globe asking me to show with my finger a trajectory of a (nuclear) ballistic missile flying from US to China and Russia and vice versa (from Russia and China to US:)))

There should be some optimal trajectories and some general limitations on possible trajectories at all.

All I could remember that in space there are no "straight line" trajectory - only ellipses with different eccentricity.

Could you provide trajectories and some general considerations what kinds of paths are prohibited and which ones are most optimal and why?

What continents / parts of ocean / major cities :) does it fly by?

But really, I know that such trajectories are very complicated and I don't have a clue.


Here is a generic trajectory.

enter image description here

Source (see for more details)

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    $\begingroup$ non-conic (atmospheric) parts of trajectory at both ends are also very interesting! In the picture it starts exactly vertically up and then get curved (real launches also show that rocket orientates itself at some angle to "straight-up"/zenith direction a few seconds after its start. As far as I know there is a lot of controversy what that angle should be. What is that angle approximately ? $\endgroup$ – Code Complete Feb 20 '19 at 20:55
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    $\begingroup$ And why that "landing" (final) atmospheric part is not a mere continuation of that "in-space" conic (ellipse?) $\endgroup$ – Code Complete Feb 20 '19 at 20:57
  • $\begingroup$ I suggest you read the linked presentation for details. $\endgroup$ – Organic Marble Feb 20 '19 at 21:03
  • $\begingroup$ I find that presentation authoritative but pretty darn dense. Is it possible to add a sentence or two and just mention the key messages we can get from it? ("read this presentation" is not really an SE answer). Also I'm stuck wondering if $\theta_{bo}$ up through slide 14 is the same as $\phi_{bo}$ from 15 onward? Thanks! $\endgroup$ – uhoh Feb 21 '19 at 0:55
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    $\begingroup$ Antzi gave a link to a great circle mapper site gcmap.com and that might help with the "What continents / parts of ocean / major cities :) does it fly by?" part. $\endgroup$ – uhoh Feb 21 '19 at 0:58

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