One cool thing I learned about this yesterday on the NOVA episode about this mission:
Issac Newton’s famous 2nd Law of Motion (out of three) is
F = ma
In words that’s, “The size of a force on an object is equal to the object’s mass times it’s acceleration.” The more massive an object is, the more force you have to apply to accelerate it.
Mathematically, if you know any two of those values, you can calculate the third.
Newton’s 2nd Law applies to “translational motion.” Movement along a straight line. There is an equivalent formula for rotational motion, but the terms are different.
- Force is called Torque,
- Mass is called the Moment of Inertia, and
- Acceleration is called Angular Acceleration.
Conceptually it is the same though. The angular acceleration of a spinning object times its moment of inertia tells you how much torque is being applied to it.
The OSIRIS-REx mission design calls for the spacecraft to collect a target mass of material from the Bennu asteroid. It has the capability to make multiple attempts if they don’t get enough mass the first time. But how do they know how much mass of material they have collected?
The answer is they use the rotational version of Newton’s 2nd Law.
First, they turn the spacecraft on its side and stick the arm out. Then they fire the thrusters so as to start the spacecraft spinning like a merry-go-round with the arm on the outside and the main body in the center. The impulse on the thrusters (which is controlled by NASA) tells them how much torque they are applying. They then measure how fast the spinning accelerates. From those two values, they can calculate the moment of inertia of the spacecraft + Bennu material. From this moment they can calculate the mass of material. The more mass they have, the slower the acceleration will be.
That’s how you weigh things in space.