Exploring Our Universe: From the Classroom to Outer Space II. The FUSE Satellite Activity #5 Solutions

2.  Yes.

3.  Yes. The rotation would not stop.

4.  No. The sum of  the forces is zero and does not cause the center of mass to accelerate.

5.   The center of mass continues in its normal circular orbit.

6.  The directions forces of the gases on FUSE is opposite to the arrows shown in the diagram.  Therefore the direction of the turn is counterclockwise.

7.  Answers will vary. One solution is to add two more gas jets at locations opposite to those shown in the diagram.

8.  Answers will vary. One possible consequence is that the gas would interfere with the operation of the telescope.

9.  The angular momentum of the wheel increases as it turns faster.

10.  The spacecraft turns in the opposite direction!

11.  The spacecraft turns clockwise.

12.  If you slow down the wheel so that its angular speed is slower than it was when the spacecraft was not turning, it will turn if the opposite direction.

13. Make the wheel turn faster in the counterclockwise direction.

14.  The angular momentum of the reaction wheel and the spacecraft taken together is conserved. Therefore the change in angular momentum of the reaction wheel must be equal in magnitude but opposite in direction to the change in the angular momentum of the spacecraft.

I_spacecraft = 3400 kilogram meters²

I_{reaction wheel} = 0.031 kilogram meters²

D w_spacecraft = - 0.0012 radians/second
 

I_spacecraft  D w_spacecraft =  -   I_{reaction wheel}  D w_{reaction wheel}

D w_{reaction wheel}  =  1.32 x 10² radians/second  (counterclockwise)
                           = 1.3 x 10² radians/second  (counterclockwise)

                           = (1.32 x 10² radians/second) (1 revolution / 2 p) (60 seconds / 1 minute)

                           = 1.26 x 10³ rpm = 1.3 x 10³ rpm
 

a = t / I = 0.030 newton meter / 0.031 kilogram meters² = 0.968 radians/second²

 D t = D w / a  = 1.35 x 10² seconds = 1.4 x 10² seconds
 

        D q_spacecraft = 1/2 a_spacecraft (D  t)² = 0.81 radians
 

17.  To turn the telescope counterclockwise, you must turn the reaction wheel clockwise. Use a negative torque to turn the telescope through half the angle.

D q_spacecraft = 0.10 radians / 2 =  0.050 radians

a_spacecraft = 8.89 x 10^-6 radians/ second²

 Use the relationship:     D q = 1/2 a (D  t)²

D  t = 1.06 x 10² seconds = 1.1 x 10² seconds (clockwise)
 

19.  Answers will vary. Because continual fine adjustments to pointing direction are needed, the use of gas jets would require an adequate supply of gas. FUSE is not designed to be serviced while in orbit like the Hubble Space Telescope, so the gas supply could not be replenished. In addition, the gas released could interfere with the function of the spectrometer.