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Astronomy and Cosmology
Astronomy and Astrophysics
Find Trajectory from A to B: Approaches & Solutions
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[QUOTE="VladZH, post: 6063888, member: 590247"] This is problem for my video game I tried to solve a simpler problem when we don't have the body C. Let[I] P[/I]([I]r[/I],[I] φ[/I]) is a point on the circle. Let [I]s[/I] between A and P. Hence, the time for spacecraft from A to B equals Δ[I]t=s/v [/I] The time for body B to get P is Δ[I]t=Δφ/ω. [/I]We get [I][I]d/v=Δφ/ω w[/I][/I]here [I]φ=s[I]ω/v[/I][/I] Now we can find φ=φ[SUB]B[/SUB] + Δφ and direct the spacecraft towards P by a straight line. But the problem here is to express [I]s [/I]in terms of [I]φ. [/I]If we substitute [I]s[/I] by this formula we get [I]φ[/I] with cosine and [I]φ [/I]without cosine on different sides of equation [I]s = √r[SUB]s[/SUB][SUP]2[/SUP]+r[SUB]B[/SUB][SUP]2[/SUP]-2[I]r[SUB]s[/SUB]r[SUB]B[/SUB]cos([I]φ[SUB]s[/SUB]-[I]φ[/I][/I])[/I][/I] And I have no idea how to solve it Then if we consider body [I]C[/I] I thought about kind of force that pushes the spacecraft out of straight line trajectory. Moreover there are two possible trajectories near opposite sides of body [I]C[/I]. The optimal one depends on speeds of body B and speed of the spacecraft Thank you [/QUOTE]
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Find Trajectory from A to B: Approaches & Solutions
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