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08132017, 08:17 AM  #1 
Orbinaut

Elliptical trajectory from 3 points and focus?
In the pic below we have a suborbital trajectory, where one of the foci is set at the origin (0,0) and these are known: A (departure base), B (Apoapsis), C (target base) and the angle between them (from the origin). Is this information enough to determine the shape of the elliptical trajectory needed to get from A to C? What I want to find is the second focus point.
Thanks in advance. 
08132017, 03:05 PM  #2 
thing

Hi,
this seems too easy  I must have gone wrong somewhere...... I think you need to look at it in Polar terms: Code:
Let distance f1>A = b Let distance f1>B = d Let angle φ/2 = β then from R(θ) = a(1 eČ) / (1 e.cosθ) where R = distance from focus to point, a = semimajor axis, e = eccentricity, θ = angle between major axis and f1topoint line. we get: b = a(1 eČ) / (1 e.cosβ) → 1/b = (1 e.cosβ) / a(1 eČ) and (for apoapsis, where cosβ = 1) d = a(1 eČ) / (1 e) → 1/d = (1 e) / a(1 eČ) so: (1/b) / (1/d) = (1 e.cosβ) / (1 e) rearrange left hand side: d/b = (1 e.cosβ) / (1 e) d(1 e) = b(1 e.cosβ) d d.e = b b.e.cosβ d b = d.e b.e.cosβ d b = e(d b.cosβ) e = (d b) / (d b.cosβ) //Now we have e and from: R(apoapsis) = (1 + e)a then d = (1 + e)a a = d/(1 + e) //Now we have a Let distance from Apoapsis>f2 (B>f2) = m then m = a e.a = a(1 e) So, f2 lies along the line f1>B at a distance of (d m) from f1 Brian 
Thanked by: 
08132017, 03:24 PM  #3 
Orbinaut

Thank you very much!


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