Please help! 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 atalt = 202 km. The mission calls for a periapsis altitude at Mercury ofr_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 105km3/s2
Gravitational Parameter (Mercury)	M= 2.2033 x 104km3/s2
Gravitational Parameter (Sun)	S= 1.327124 x 1011km3/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 inAUandkm.

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.,2:2:25:23or2 days, 2 hr, 25 min, 23 s). Use 4 decimal places in your calculations, none required in the final answer.

3. Calculate the energy () for this Hohmann transfer ellipse. Express your answer in bothAU²/TU²andkm²/s².

4. Calculate the Sun-relative velocity (v₁) at Earth departure (Aphelion on the Hohmann transfer). Express your answer in bothAU/TUandkm/s.

5. Calculate the Earth-relative hyperbolic excel velocity (v⁺). Express your answer in bothAU/TUandkm/s.

6. Calculate the launch energy (C₃) required for this mission. Express your answer in bothAU²/TU²andkm²/s².

7. Calculate the energy of the Earth-departure hyperbola (_E). Express your answer in bothAU²/TU²andkm²/s².

7. Calculate the circular parking orbit velocity (v_LEO) and the perigee velocity (v_p) of the Earth-departure hyperbola.Express your answer inkm/s.

8. Determine the velocity impulse (v_TMI) needed in the LEO for the "trans-Mercury injection" (TMI).Express your answer inkm/s.

9. Calculate the Sun-relative velocity (v₂) at Mercury's SOI (perihelion on the Hohmann transfer). Express your answer in bothAU/TUandkm/s.

10. Calculate Mercury's orbit velocity (v_M). Express your answer in bothAU/TUandkm/s.

11. Calculate the Mercury-relative hyperbolic arrival velocity (v). Express your answer in bothAU/TUandkm/s.

12. Calculate the B-plane offset distance (d) for the target periapsis altitudealt_p= 122 km.Express your answer inkm.

13. Compute the spacecraft's velocity at periapsis passage (v_p).Express your answer inkm/s.

14. Calculate the low-Mercury orbit speed (v_LMO) for the circular orbit of the spacecraft.Express your answer inkm/s.

15. Calculate the impulse (v) required for insertion into a circular Mercury orbit.Express your answer inkm/s.