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Can you find the Keplerian elements and the necessary changes of velocity for this transfer orbit?
A spaceship is initially in Earth's orbit, but is on the opposite side of the sun from Earth. Its captain wants to enter a transfer orbit, bound for Vesta, at 12h UT on 26 June 2017. The navigator does some trial runs on a computer and discovers an elliptical transfer orbit having its aphelion at Vesta upon arrival at 4h 45m 36.036s UT on 12 June 2018.
Check the navigator's work to ensure that an elliptical transfer orbit does exist for these times for departure and arrival. Show the elements of the transfer orbit and the delta-vees required for transfer orbit insertion (departure) and for matching velocity with Vesta at arrival.
Spaceship initial orbit
a = 1.000002 AU
e = 0.016711
i = 0.0°
Ω = 0.0°
ω = 103.095°
T = JD 2454285.96
Vesta's orbital elements
a = 2.36126914 AU
e = 0.089054753
i = 7.13518389°
Ω = 103.91484282°
ω = 149.85540185°
T = JD 2454267.1969204
Departure time,
t₁ = 12h UTC, 26 June 2017
Arrival time,
t₂ = 4h 45m 36.036s UTC, 12 June 2018
Show that a transfer orbit exists that will permit the spaceship to intercept Vesta.
Find the Keplerian elements of the transfer orbit.
Find the change of velocity needed at departure for transfer orbit insertion.
Find the change of velocity needed to match velocity with Vesta at arrival.
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