Exploring Our Universe: 
From the Classroom to Outer Space
II. The FUSE Satellite
Activity #5
POINTING FUSE: CONSERVATION IN ACTION
STUDENT ACTIVITY

Turning in Space

Videos of astronauts in space doing ordinary things are fascinating because objects on orbiting satellites do not behave like objects on the surface of Earth. The objects look like they are floating, nothing falls down, and the astronauts can perform tumbling exercises that would be impossible on Earth. "Weightlessness" is the word often used to describe the condition of objects in space. This term is misleading because, although an astronaut in orbit standing on a conventional scale would read zero as her weight, the gravitational force of Earth pulls almost as strongly on the astronaut in space as it does on the astronaut when she is on Earth. The reason the scale registers zero is that both the astronaut and the scale are pulled toward the center of Earth so that they have the same acceleration. Such objects, free to fall under the attraction of the force of gravity, are said to be in "free fall" and appear to move as if they experience no gravitational force. In contrast, on the surface of Earth, the surface supports the scale which, in turn, pushes up on the astronaut, registering her weight. In order to understand how the FUSE spacecraft is controlled, you must imagine yourself to be in the "weightless" environment of orbit.

In order to complete its scientific mission, the FUSE telescope must be able to turn to point at a variety of distant astronomical objects and it must be able to make continuous delicate adjustments to its direction. It is your job to design the mechanism that steers the FUSE spacecraft and you will have to draw on your knowledge of basic physics principles to accomplish your task. You will consider two possible mechanisms for turning FUSE: gas jets and reaction wheels. This exercise leads you through the physics of both and shows why the second mechanism was chosen for the FUSE mission.

To complete this exercise you will need a calculator and your imagination. You may find it useful to do the suggested demonstrations and to read about torque and angular momentum in your textbook.

 

Practice on a Pencil

Lay a pencil on a flat smooth table and try pushing it with one or two fingers as indicated in the sketches below.
1. In which cases does the object rotate?
2. Does the rotation stop?
3. Would your answers be different in the “weightless” environment of space? Why?

Figure 1  Four ways to push a pencil.










Often when we describe the motion of a large object, we treat the object as if all of it is located at a single point, its center of mass. This is exactly what you did in earlier activities when you did calculations for FUSE in its orbit. In this exercise we will have to consider the motion in more detail because we are concerned with turning the satellite. In general, the motion of an extended object can be analyzed in two parts: motion of the center of mass and rotation of the object around the center of mass. In this exercise we will deal with the second part: the rotation of FUSE.
 

 
Listed here are the relationships you will need in this exercise. Check the glossary for unfamiliar terms. Note that vector quantities are written in boldface.
 
The angular momentum of an object is the product of its moment of inertia and its angular velocity.
L = I w
L is the angular momentum
I is the moment of inertia
w is the angular velocity.
Angular momentum is a vector quantity as is angular velocity. In this exercise we will use “-” to show clockwise rotation and “+“ to show counterclockwise rotation. The angular momentum of an object is equal to the sum of the angular momenta of its parts.
The rotational equivalent of Newton's Second Law is that the net torque acting on an object is equal to its moment of inertia times its angular acceleration.
t = I a
t is the net torque
I is the moment of inertia
a is the angular acceleration.
One consequence of this relationship is that if the net torque on an object is zero, its angular velocity does not change and its angular momentum is conserved. For an object is made up of two parts, this means that if the angular momentum of one part changes, the change of angular momentum of the other part must be equal in magnitude and opposite in direction so that the sum of the changes is zero. Another consequence is that if the net torque acting on an object is constant, so is the angular acceleration.
Constant angular acceleration is equal to the change in angular velocity divided by the time it takes to change.
a = D w / D t
a is the angular acceleration
D w is the change in angular velocity
D t is the elapsed time.

Gas Jets

Picture the FUSE satellite in orbit in space as a long box. Imagine attaching two canisters of gas as shown in Figure 2. If identical puffs of gas are released in the directions shown by the arrows:
4. Will the motion of FUSE’s center of mass be affected by the release of the gas? Why? Hint: Consider Newton's Second Law of Motion.
5. Describe the motion of FUSE’s center of mass as seen from Earth.
6. In what direction will FUSE turn? Hint: Consider the direction of the force on the canister due to the escaping gas. If you are not sure, try letting the gas escape from a balloon and note the direction of the force on the balloon.
7. How would you stop the turn assuming you could add more equipment to the satellite? Note that the satellite will keep turning unless additional torque is applied.
8. What are the possible consequences of putting such gas jets or a small rocket motor on a spacecraft such as FUSE?
 

Figure 2. A simple representation of the satellite with two gas jets added. The “X” marks the position of the center of mass.



Reaction Wheels

A reaction wheel is a spinning disk that is secured to the satellite with brackets that allow the disk to spin with a minimum amount of friction. A motor that gets its power from solar panels is attached so that the angular speed of the wheel can be changed. Figure 3 shows FUSE represented by a rectangle with one reaction wheel attached to the spacecraft. Note that the sketch distorts dimensions and position.

Figure 3   A representation of FUSE with one reaction wheel.

To understand how FUSE turns, consider all of FUSE to have just two parts: the spinning disk and the rest of the spacecraft. Assume that initially the wheel is spinning counterclockwise, in the direction of the arrow, but the spacecraft is not rotating. Ignoring the effects of the thin atmosphere, there is no external torque acting on FUSE and therefore, its angular momentum does not change. Turning the motor on or off generates compensating internal torques so the net torque is still zero.
 
 

9. What happens to the angular momentum of the wheel if the motor causes the disk to turn faster?

 

10.  What must happen to the rest of the spacecraft to keep the angular momentum of the whole FUSE system constant?
 

11. So if the wheel spins faster, in what direction does the spacecraft turn?
 

12. How would you get the spacecraft to turn in the opposite direction?
 

13.  How would you get the spacecraft to stop if it was initially turning counterclockwise?


 
 

Test Your Understanding

Assume the moment of inertia of a reaction wheel in FUSE is 0.031 kilogram meters and the moment of inertia of the rest of the spacecraft is 3400 kilogram meters. Also assume the motor can apply a constant torque of ±0.030 newton meter to the reaction wheel.
 
14. What must be the change in the angular velocity of  the reaction wheel  to cause the spacecraft to turn clockwise at angular speed 0.0012 radians/second? What is this change in RPM (revolutions per minute)?  (Assume the spacecraft  is not turning initially.)
 
 
 
 

15.  How long will it take the reaction wheel to reach the angular speed calculated  above?
 
 
 
 

16. Through what angle has the spacecraft turned during this time? (Remember this is constant acceleration, not constant speed. When an object moves with constant linear acceleration from rest, the distance it travels is equal to one half the product of its acceleration and the square of the time.  When an object turns from rest with constant angular acceleration, the angle through which it turns is given by one half the product of its angular acceleration and the square of the time.)

 
17. To capture the light of a distant quasar, you must rotate the telescope so that it turns through angle of  +0.10 radians (5.7o) and stops. Describe how the reaction wheel motor must be operated to acheive this. Specifically, calculate the time the constant torque motor should be operated to turn the reaction wheel in each direction and specify the direction.
18. Why do satellites carry at least three reaction wheels?  How are they oriented in the spacecraft?
19. Why do you think reaction wheels were chosen over gas jets to make FUSE turn?
Note:  To answer the other questions in this activity, you have assumed there are no external forces acting on the spacecraft. To answer this question you should know that there are small external torques due to three sources:  the aerodynamic drag of the residual atmosphere, gravity gradients (the small difference in the gravitational pull of Earth on opposite sides of the spacecraft, and very small magnetic torques due to interaction of Earth's magnetic field with magnetic materials and current carrying wires within the spacecraft.