Originally posted by: Cogman
Originally posted by: Cattlegod
Originally posted by: FleshLight
Originally posted by: DrPizza
Holy shit, that's a hard problem. You do know that the earth is, more or less, spherical, don't you? So, what do you mean by a straight line? Through the earth?! Ouch!
A straight line is going to be an arc. Wow, what grade level are you in? That's a really really hard problem!
Truth. We need the altitude of the plane and the projected coordinate system you are using.
not to mention starting height, because we could make it efficient and fly in a straight line still if it started high enough.
Also need starting speed and type of plane so we can determine how long it takes to get up to cruising speed. if it is a 1940's prop plane and starting at 40,000 feet, they guy may freeze to death and thus never make it to the destination.
Don't forget, air friction, cross winds, the fact that he is burning fuel (So the plane gets lighter as he flies). Also, you can't forget tidel differences, and the fact that the position of the moon and sun can change the amount of energy expended on the trip.
It looks like you'll have to break out some Calc 2 to get this problem, its the only way to be sure.
I suggest looking into triple integrals, the gravitational constant, and maximizing equations. Good luck.