Now this is one I have been wondering about at least since high school.
When I was still in hs, we were taught mass is usu. measured by “comparing” it to other masses on a scale. That is at least the way we were taught to do it. Modern scientists may have other ways too, I’m sure.
But how do you measure mass in a weighless environment? There no weight. So there is no way to compare it to other masses, right? And also, I guess part of my question is, what properties to masses retain even in a so-called weighless environment?
My ignorant supposition is that you’d apply an equal force to it and a reference mass and compare the resulting accelerations. That force doesn’t have to be gravitational; it could be whatever.
This is precisely right. Force is mass times acceleration, so mass is force divided by acceleration, so as long as you know the force, and can measure the acceleration, you can determine the mass.
This is also what you do with a bathroom scale, only in that case the acceleration is the acceleration due to gravity, and the force is your weight.
You could also measure the gravitational force exerted by the unknown mass on some known mass, or you can measure the motion of some gravitationally bound system (a star and a planet, or a binary star system) to get mass estimates, or you can go a more indirect route, for instance, using the link between a star’s mass and its luminosity and thus determine its mass via the Hertzsprung-Russel diagram.
But in most everyday situations*, applying a force and measuring the acceleration is probably the most straightforward thing to do…
*Well, all those everyday situations taking place in zero g, at least…
It’s possible – if you’re careful and clever – to measure the gravitational attraction between two kilogram-sized objects even here on Earth. So that should be possible in microgravity as well.
In fact, all these tests work the same way, using f = ma.
In the case of a scale, F is gravitation, and a is … well, if you belive Einstein, the acceleration imposed by the table or floor or whatever. Yup, seems odd to me too!
In all the other cases, it’s a pretty clear force and pretty clear acceleration. You either apply an acceleration and measure the force, or vice versa.
A centrifugal scale provides a constant acceleration, and measures the centripital force. A linear scale might provide a constant force and measure the acceleration, but that would be trickier.
This. Here on Earth, the acceleration due to gravity is the known force. In a weightless environment, apply some other known force.
You might also be able to measure by putting objects in orbit around each other and measuring what happens to the orbit. Make sure you don’t have too many massive objects nearby to prevent the results from getting skewed too much.
You find the caretaker and offer him the barometer as a gift if he will tell you its mass. If he refuses to cooperate, you bludgeon him with it until he’s ready to talk.
Take a spring of known stiffness, attach it to the mass, extend the spring and measure the acceleration of the mass. This assumes you have an “immovable” object to attach the spring to, so works best for smallish masses in a largish spacecraft.
Some other methods (most assume a certain other property is known and the mass is small size )
A. Equivalent of titration : If you know the what the mass is made of and it dissolves in say a certain acid, you can titrate to find mass.
B. Electrical charge : You can charge the mass and move it in a constant electric field and measure the resulting deflection. (this is sort of F=ma equivalent)
C. Substitute B with magnetic field
D. If you know the specific heat of the body, you can thermall connect it to a known mass and specific heat body and then measure the resulting temperature, This will give you the mass of the body
E. Spin the body on its on axis to a known velocity - measure the resulting kinetic energy by slowing it down by friction (say in a body of water) - measure the temperature rise in water.
This is exactly what is done, at least on the NASA Skylab missions. Astronauts aboard the Skylab station used what is called an M172 Body Mass Measurement Device to measure their mass, as inidcated in the link from CalMeacham. The function of this device is described in this newsletter from Tom Irvine’s VibrationData.com site (which has a large amount of highly useful information about launch and space vehicle dynamic environments as well as general information on vibration and vibroacoustics), but essentially it treats the astronaut and chair as a lumped mass of an undamped single degree of freedom (1DOF) system and then calculates the mass from the response period after release from an enforced displacement via the equation for the simple harmonic oscillator, ω[SUB]n[/SUB]=√(k/m), where ω[SUB]n[/SUB] is the natural frequency of the system, k is the spring constant, and m is the mass. In other words, the astronaut compressed and released the spring, and the resulting time it took for the chair-spring system to go through one cycle of extension and retraction allows one to calculate the mass of the system. (The exact calculation of mass is m = k∙T[SUP]2[/SUP]/(4∙π[SUP]2[/SUP]), where T is the measured period of one cycle.) Although the Irvine newsletter doesn’t talk about the effectiveness, it was apparently precise enough to measure astronaut mass to within less than a pound. This is obviously more practical than a centrifuge large enough to spin an astronaut.
Determining mass via displacement of water, i.e. Archimedes principle, is not practicable because this a measure of force resulting from the acceleration due to gravity. In lieu of gravity, you would have to apply a known acceleration from thrust or rotation, and then you could just measure the resulting “weight” (e.g. inertia from the Lagrange–d’Alembert principle) directly.