Question: 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
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 (vTMI) in from a circular low-Earth orbit atalt = 202 km. The mission calls for a periapsis altitude at Mercury ofrp= 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 (tH) 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 (vLEO) and the perigee velocity (vp) of the Earth-departure hyperbola.Express your answer inkm/s.
8. Determine the velocity impulse (vTMI) 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 (vM). 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 altitudealtp= 122 km.Express your answer inkm.
13. Compute the spacecraft's velocity at periapsis passage (vp).Express your answer inkm/s.
14. Calculate the low-Mercury orbit speed (vLMO) 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.
Step by Step Solution
There are 3 Steps involved in it
Get step-by-step solutions from verified subject matter experts