Astronomy
Two burns to a new orbit
Raise an Earth orbit, or fly the same two burns to the Moon, Venus, Mars or Jupiter: the phasing, the launch window, the burn from the parking orbit and the capture at the other end, and the bi-elliptic alternative.
The model and its limits
Two impulsive tangential burns between coplanar circular orbits about one centre (the Earth, or the Sun with the catalogue's semi-major axes as circles). Departure and capture are patched conics with v∞ from the heliocentric impulse; windows from mean longitudes, not from a pork-chop search. No finite burns, drag, plane changes or eccentric planet orbits.
Equations used in the module
Equations a_t = (r₁+r₂)/2; Δv₁ = √(μ/r₁)[√(2r₂/(r₁+r₂))-1]; t_t = π√(a_t³/μ) Δv_park = √(v∞² + 2μ_E/r_p) − √(μ_E/r_p); Δv_capture = √(v∞² + 2μ_t/r_c) − √(μ_t/r_c); T_syn = 1/|1/T₁ − 1/T₂|
