calculations.md

List of formulas used in making scripts.

orbital velocity vector == vOV orbital position vector == vOP eccentricity vector == vE

true anomaly == tA mean anomaly == mA eccentric anomaly == eA

apoapse == ap periapse == pe eccentricity == e

arg. of periapse: argPe

precision == p

true anomaly at current location

if vOV * vOP >= 0 arccos({vEvOP}/{abs[vE]*abs[vOP]}) else -[-2pi+arccos({vEvOP}/{abs[vE]*abs[vOP]})]

eccentricity from ap and pe

(ap+pe)/(ap-pe)

eccentric anomaly from true anomaly and eccentricity

arcsin([sqrt{1-e^2}sin{tA}]/[1+ecos{tA}])

mean anomaly from eccentric anomaly and eccentricity

eA- e sin eA

eccentric anomaly from mean anomaly

initial guess == (180-mA)/2

f(eA) == eA - esin(eA) - mA f'(eA) == 1 - ecos(eA)

eA - [(eA - esin(eA) - mA)/(1 - ecos(eA))]

iterate for either desired precision or fixed number of iterations

true anomaly at ascending node

2pi - argPe

true anomaly at position "north"

(tA at AN) + pi/2 if result > 2pi result-2pi

ETA to position of given mean anomaly

avgAngSpeed == 2pi/orbital_period

((targetmA - currentmA)/avgAngSpeed) + timenow == timeattarget

timeattarget - timenow == ETA to target