How to project an arbitrary elliptical orbit onto the night sky plane?
The (x, y, z) position of an object on its orbit with reference to a reference plane are given by:
u = ω + ν
x = r (cos Ω cos u − sin Ω sin u cos i)
y = r (sin Ω cos u + cos Ω sin u cos i)
z = r sin i sin u
(MEEUS, Jean. Astronomical Algorithms, Second Edition, p. 233)
This should help you find what you need.