Measuring mass without gravity
In free fall nothing has weight, so a scale reads zero. But mass doesn't vanish: it shows up as inertia. The simulator ties two objects together and spins them around their center of mass to compare them.
Key formula
x_cm = (m₁·x₁ + m₂·x₂) / (m₁ + m₂) · r₁ / r₂ = m₂ / m₁
Try it
How to use the simulator
In free fall a scale is useless, because nothing has weight. Mass is still there, though, and it shows up as inertia. Tie two objects together and spin them, and the pair rotates around its center of mass, which sits closer to the heavier one. When the masses are equal, the center is right in the middle and the system spins evenly.
Controls
- Water (mL = g): the amount of water in the reference bag. One milliliter of water has a mass of one gram.
- Object (g): the mass of the object you want to measure.
Things to try
- Recreate Grace's experiment: adjust the water until it balances a 328 g object. The system counts it as balanced once the difference is under 5 g.
- Make the masses very unequal and watch the system shift toward the heavier side.
- Think about precision: 325 versus 328 g is an error of about 1%, excellent for an improvised instrument.
Loading simulator…
Weight and mass are not the same
Mass is the amount of matter and an object's resistance to changes in its motion. Weight is the force with which gravity pulls on that mass. On Earth they always go together, which is why we mix them up, but in an orbiting craft or deep space apparent weight disappears while mass stays the same.
Getting a 100 kg crate moving on the Space Station takes as much push as on Earth: the only thing you don't have to overcome is its weight.
The center of mass
Tie two objects with a string and spin them in weightlessness, and they rotate around a point called the center of mass. That point sits closer to the heavier object, at distances inversely proportional to the masses. If the masses are equal, the center is right in the middle and the system spins evenly.
That lets you compare an unknown mass with a known one, such as a bag of water (one milliliter of water has a mass of one gram): you adjust the amount of water until the spin is balanced.
How astronauts weigh themselves
On the International Space Station, astronauts are measured with a device that pushes them with a spring of known force and measures the acceleration they get: by Newton's second law, m = F/a. Other systems use the oscillation of a spring, whose period depends on the mass riding on it.
Worked example
Example: two masses on a 1 m string
- Tie a 600 g object and a 200 g object with a 1 m string and spin them.
- Distance from the center of mass to the 600 g object: 1 · 200 / (600 + 200) = 0.25 m. To the 200 g one: 0.75 m.
- The light object traces a circle three times bigger. If the masses were equal, each would circle 0.5 m from the center.
- In the simulator, match the water to a 328 g object: the system counts as balanced once the difference is under 5 g.
In Project Hail Mary
In the novel, the main character has to measure an object's mass somewhere without gravity, and does it by comparing it with a known amount of water through spinning.
Frequently asked questions
Is there no gravity on the Space Station?
There is: at 400 km altitude gravity is about 90% of its surface value. Astronauts float because they and the station are falling around Earth together all the time, in free fall.
Would a pan balance work on the Moon?
Yes, because it compares two masses under the same gravity. A spring scale, on the other hand, would read one sixth of normal.
Why does weighing astronauts matter?
In weightlessness they lose muscle and bone mass, and doctors need to track that loss to adjust exercise and diet.