I think first that would mean you want to minimize final mass - ok also can maximize exhaust velocity and can minimize drag through atmosphere and take optimal advantage of Earth’s rotation to include in your initial speed -so launch east at equator - good question!

I'm so happy you found this material and that you find it useful!! I hope you also found the answers to those problems from the workbook are also available, scroll down the page a little. About imperial units , I think it's important to be able to work with both - in fact, on this topic, interesting that engine "Isp", which is "specific impulse" is measured in seconds- to be common unit in both metric and imperial. But converting units is such an important skill in general, its important to learn to convert units of all kinds quickly, sometimes convert by hand, sometimes just use google calculator, practice that and you'll get faster and better at it, and that skill transfers to other things, looking at dimensional analysis is a way to make sure you understand concepts - good luck with studying and let me know if you have any questions

not sure I understand, masses in a gravity field don't have to solve anything - it's just calculus that helps us "solve" or at least describe the behavior... and I agree, its fascinating how complicated things get when we consider 3 bodies or more - and this has nothing to do with relativity.. and even calculus still works in systems of 3 or more bodies, it's just not producing simple elegant formulas like it was with 2 bodies... all pretty amazing... thanks for your feedback

you can see the methods of calculus solving the 3 body problem very precisely in this more recent video I did kzbin.info/www/bejne/o2S6ZWqGgL2gj7s

@@csvaughen what I meant is, try to come out with a method that is identically simple, but with a result that matches GR rather than Newtonian mechanics.

thank you!!!! So glad you find it valuable! It was a super fun project ... probably you saw sites.google.com/view/kspmath but if not, check it out

maybe the first discovery of chaotic behavior in math and physics

yes - good points - I did this in another video here kzbin.info/www/bejne/o2S6ZWqGgL2gj7s

great question - add thrust - I do not know what happens... I do recall that planes can be designed specifically to damp out this kind of oscillation over time, and after quick query to chatgpt and it says it is theoretically possible to have a continuous oscillation that goes on forever under the right conditions

haha, yes - and 8 years later, computer is still near the kitchen

whoa! yes - I'm definitely checking that out! thanks

Thanks!!! well, probably you'd eventually get to this in school doing aerospace or astrophysics, for example check out "Orbital Dynamics for Engineering Students" by Howard Curtis

it doesn't predict locations where eclipses will be visible

@@csvaughen when it shows the fases of the moon and we can see both the sun and moon move then it shouldnt be impossible to predict the eclypses

@@csvaughen furthermore, i believe the cardinal directions are different from what we have been taught. At least the book of enoch tells us that they are (starting at the top) west, north, east, south. With these fixed and using a FE map such as the one from david rumsey. We might be able to figure out the locations as well.

@@MusicComposerZenki it's an interesting topic, to learn more we can test theories with falsifiable predictions. Check out this video on eclipses: kzbin.info/www/bejne/fZvFlphpd92SrtUsi=sTwLJmhMx8Y83jwz which also reminds me of one of my own videos on the topic: kzbin.info/www/bejne/i3SXYZ56paZ8bq8

Vibes of cosmos

Yes good points- thank you

yes!!! I'm so happy you liked it - and yes it IS confusing - takes a while to get used to

@@csvaughen I should say, it’s only because Ive studied Astronomy for a number of years I got it quickly, or some of it… now back to the drawing board.. 😀 You did an excellent job of explaining it, verbally and visually. 🔥 10/10 with Gold Stars ⭐️⭐️⭐️⭐️⭐️

yes, that's right, equation of a circle, centered at origin, with radius 4

thanks for the feedback, but I think you are making an error by using lat = e - 90 + d. It should be either 90-e+d (northern hemisphere, and the choice for Cook) or 90-e-d (southern hemisphere) so this does require knowing which hemisphere you are in, but there are many natural cues for that.

@@csvaughen Your second formula doesn't reflect signs very well. I watched the derivation you provided and noticed that in your 'southern hemisphere' example you take positive theta for a latitude south of the Equator. So using your second formula 90-e-d, you get -8.5 deg, but since you considered theta positive for southern latitudes, then -8.5 deg would be 8.5 deg North. Also, one more thing: The criterion that decides which formula to use is NOT whether you are N or S of the Equator but rather whether you are N or S of 22.9 degrees (the parallel corresponding to the declination). It would be as you say when dec=0 (on the equinoxes).

yes, very true

thanks, I can try answering any questions, this is a newer video on same topic kzbin.info/www/bejne/Y2fMo5enhNSCY5o

Hi, thank you for your comment- I'm sorry, I'm not even familiar with the Nanson method - had to look that one up - interesting - a hybrid method!

yes, fascinating to think about: the "bodies" measured by something other than mass and the "interactions" governed by something other than gravity. It seems like going from 2 to 3 bodies would always significantly complicate the interactions and this example, with mass and gravity, is just one illustration of that.

kzbin.info/www/bejne/nKvcf6d4mpZ7a7c