How do we weigh objects in space?
How do you weigh objects in space without gravity?
There is a simple answer to your question: we don't, because in space where there is no gravity objects weigh nothing! We have to be carefull about definitions. The weight of an object is a force. It is the force with which a body is attracted toward Earth or another celestial body. This means that when you are in space, away from Earth, objects do not weight anything since they do not feel gravitational attraction to the Earth.
What objects have though in space is mass. This is because mass is defined as the amount of material an object contains, and that doesn't change whether the object is on Earth, on the Moon, or anywhere in space.
Now, weight and mass are linked in the following way: the weight is obtained by multiplying the mass by the value of the gravitational acceleration. That means that for an object of a given mass, the stronger the gravitational attraction, the larger its weight (this is why objects weigh 6 times more on Earth than on the Moon, and weigh nothing in empty space). On Earth we know the value of the gravitational attraction, so a measure of the weight (which is what a regular scale measures) gives us directly the mass. This is why in the common language weight and mass are often confused. But it space it makes a big difference. Objects can have a large mass, but weight nothing.
So how do we measure mass in space? On Earth we only have to weigh the object and divide by the gravitational acceleration, but this obviously doesn't work in space. To measure mass in space, we have to use another kind of scale, which is called an inertial balance. An inertial balance is made of a spring on which you attach the object whose mass you're interested in. The object is therefore free to vibrate, and for a given stiffness of the spring the frequency of the vibrations enables the scientists to calculate the mass.
This is how you would get the mass of objects in a space shuttle, or something lke it. But there are other objects in space that astronomers are very interested in knowing their masses: stars and galaxies. The way to get the mass of these objects is to look at the gravitational interaction with other objects nearby. For example, if you have two stars orbiting one another and you know the distance between them and how long it takes for one to go around the other, you can calculate the mass of the stars. Similar tricks apply to measure the mass of galaxies, for example by measuring how fast they rotate.
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