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Question: Assume the crew module has a moment of inertia of ...

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Assume the crew module has a moment of inertia of Icm = 232 × 10^6 kgm2 . The necessary angular acceleration of the command moule to spin up to the desired rotational velocity during the first round trip to mars is cm = 6.37 × 10^9 rad/s^2 .

1. If it is spun up using a pair of ion thrusters mounted around the perimeter of the central core, which has a diameter of d = 5.0 m and they provide a thrust at an angle of t = 35 relative to the tangential direction, what magnitude of torque must they provide to the spacecraft to achieve the required angular acceleration?

2. How much force must each thruster provide? The crew module part of the spacecraft is rotating with an angular velocity of H = 0.43 rad/s when a surface transport shuttle approaches it. The shuttle has a mass of ms = 1.8 × 10^6 kg, and has a velocity of vs = 18 m/s in a direction that is s = 125 from the radial axis of the Hermes as shown. It attaches to the docking bay on the trailing edge of the crew module a distance rs = 15 m from the central axis of the Hermes ship.

3. After it is docked, what is the angular velocity of the crew module?

4. What would you feel if you were in the crew compartment of the Hermes when the shuttle docked?

Explanation / Answer

a) torque provided to the spacecraft is

T = I *

   = (232*10^6) * (6.37*10^-9)

   = 1.478 N.m

b) force provided to thruster must be

T = r * F * sin

F = T / (r * sin )

   = 1.478 / (2.5 * sin 35)

= 1.031 N

c) Angular momentum by shuttle = r x mv

                                               = 15* sin s x mv

                                               = 15*sin 125 * (1.8*10^6) *18

                                               = 39.812*10^7

Initial angular momentum = H * Icm

                                     = 0.43 * ( 232 × 10^6)

                                     = 9.976*10^7

Final Angualr momentum = 39.812*10^7 + 9.976*10^7

                                      = 49.78*10^7 kgm^2 / s

Final Angualr velocity = 49.78*10^7 / 232*10^6

                              = 2.15 rad/s

d) I would feel sudden jerk

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