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NASA is planning to send a spacecraft from Earth to Mercury. For the purposes of this assignment, let's assume a coplanar transfer between circular planetary orbits and there is no gravitational influence from Venus. Assume the upper stage of the launch vehicle performs the Trans Mercury Injection (v_TMI) in from a circular low-Earth orbit at alt = 202 km. The mission calls for a periapsis altitude at Mercury of r_p = 122 km. Unless otherwise noted, use 4 decimal places in your calculations and answers, as applicable.

Use the information below regarding the parameters for this assignment:

Gravitational Parameter (Earth)	E = 3.986 x 105 km3 /s2
Gravitational Parameter (Mercury)	M = 2.2033 x 104 km3 /s2
Gravitational Parameter (Sun)	S = 1.327124 x 1011 km3 /s2 (1 AU3 /TU2)
Semimajor Axis (Earth)	rE = 1.0000 AU
Semimajor Axis (Mercury)	rM = 0.3871 AU
Canonical Units (1 AU)	1 AU = 149597871 km
Canonical Units (1 TU)	1 TU = 5022643 s (58.1324 days)
Canonical Units (1 AU/TU)	1 AU/TU = 29.7847 km/s

1. Calculate the semimajor axis for this Earth-Mercury Hohmann transfer. Express your answer in AU and km. (6 Points)
2. Calculate the flight time (t_H) for the interplanetary cruise of this Hohmann-transfer ellipse. Express your answer in days, hours, minutes, and seconds (i.e., 2:2:25:23 or 2 days, 2 hr, 25 min, 23 s). Use 4 decimal places in your calculations, none required in the final answer. (6 Points)
3. Calculate the energy () for this Hohmann transfer ellipse. Express your answer in both AU²/TU² and km²/s². (6 Points)
4. Calculate the Sun-relative velocity (v₁) at Earth departure (Aphelion on the Hohmann transfer). Express your answer in both AU/TU and km/s. (7 Points)
5. Calculate the Earth-relative hyperbolic excel velocity (v⁺). Express your answer in both AU/TU and km/s. (6 Points)
6. Calculate the launch energy (C₃) required for this mission. Express your answer in both AU²/TU² and km²/s². (6 Points)
7. Calculate the energy of the Earth-departure hyperbola (_E). Express your answer in both AU²/TU² and km²/s². (6 Points)
8. Calculate the circular parking orbit velocity (v_LEO) and the perigee velocity (v_p) of the Earth-departure hyperbola. Express your answer in km/s. (7 Points)
9. Determine the velocity impulse (v_TMI) needed in the LEO for the "trans-Mercury injection" (TMI). Express your answer in km/s. (6 Points)
10. Calculate the Sun-relative velocity (v₂) at Mercury's SOI (perihelion on the Hohmann transfer). Express your answer in both AU/TU and km/s. (7 Points)
11. Calculate Mercury's orbit velocity (v_M). Express your answer in both AU/TU and km/s. (6 Points)
12. Calculate the Mercury-relative hyperbolic arrival velocity (v). Express your answer in both AU/TU and km/s. (7 Points)
13. Calculate the B-plane offset distance (d) for the target periapsis altitude alt_p = 122 km. Express your answer in km. (6 Points)
14. Compute the spacecraft's velocity at periapsis passage (v_p). Express your answer in km/s. (6 Points)
15. Calculate the low-Mercury orbit speed (v_LMO) for the circular orbit of the spacecraft. Express your answer in km/s. (6 Points)
16. Calculate the impulse (v) required for insertion into a circular Mercury orbit. Express your answer in km/s. (6 Points)