This is a good general rule of forum etiquette, for pretty much any forum. While the following link is probably a little strident
for a forum such as this one, it does provide valuable food for thought about the process:
To elaborate a bit on that, you can determine an object's mass by observing how it influences other objects. In a two-body system, gravity produces a force that is proportional to the product of the masses of the two bodies and inversely proportional to the square of the distance between them. For a small object to orbit a larger one, it must travel at a particular velocity given a particular distance or it will either spiral in and impact the large object, or zoom away into space. (Oversimplifying here, but the point is that the orbital velocity of an object is a result of how massive the parent object is and how far away the object is from the parent.)
If the two objects are very far apart in mass, you can pretty much ignore the mass of the smaller object as negligible (for instance, the mass of a satellite versus the mass of the Earth). Once you throw that out, if you know the distance and motion of the smaller body, you have an equation that you can solve to work out the mass of the larger object. This has been used to measure the masses of many bodies within our solar system, so it's very well tested experimentally.
So how do we measure the mass of the central black hole? First, we can't do it by measuring the Sun's motion. Remember the inverse square rule -- the farther away you get, the less the force is until eventually it's effectively nil. At our distance from the galactic center, we cannot detect any force whatsoever from the central black hole. It's also totally swamped by the gravitational attraction from the rest of the galaxy, which is considerably more massive and a lot more spread out. So we have to find something that orbits the black hole itself, which is far enough from the hole for our telescopes to be able to resolve it, and which is close enough that it will move fast enough for us to be able to actually measure its motion. Turns out, there are a few stars which fit the bill. They can only be observed in infrared, which penetrates the thick dust lanes between us and the galactic center. They travel extremely fast -- a significant fraction of light speed, so fast that in just a few years, they can be easily seen to have moved. (That's not the case for stars out here, where we mostly have to rely on redshift to figure out their speed.) Scientists have estimated their velocity and distance from the object they orbit, and from that, deduced the mass of the mystery object. And it's staggering -- it's estimated to be about 10 million solar masses. That pretty much has to be a black hole, and a freakin' huge one at that.
How does the mass indicate that it's a black hole? A black hole isn't actually anything supernatural. It's just a really dense object, so dense that the math for gravity gets really weird. It just has to be dense enough that there is some altitude above its surface where the escape velocity is light speed, and where the gravitational forces within the object, compressing it, exceed all known forces that could cause it to retain a shape. So it's exotic, but not magical. If an object is sufficiently dense, it's a black hole. And ten million solar masses should take up a hell of a lot of space, but we don't see them. We know it's smaller than the orbit of those super-fast stars at the center of the galaxy -- a lot smaller. If you do the math, just being smaller than that means it's gonna collapse into a black hole.
So yes, we really do have a black hole at the center of our galaxy!
They spent years studying the stars near the centre of the galaxy, and found them to be orbiting an invisible mass. Their orbits allow astronomers to predict the mass of the invisible object and it seems to be a good candidate for a black hole.
In space, bigger objects may round up smaller objects, but not always. It depends on how far apart they are.
Gravitational attraction diminishes according to the inverse square law. That is to say, as you move farther away from the big object, its attraction decreases exponentially. Consider the Earth. It's pretty massive, right? It keeps you firmly attached to it. It even holds the Moon, a distant and massive object, in orbit around itself. But if you go far enough away, the gravitational attraction of the Earth diminishes so much that you cannot measure it.
There's another factor: speed. If you're going fast enough as you pass by a massive object, it can't capture you. This is because the acceleration it produces on you is not enough to turn you around -- it may affect your path or speed, but it won't capture you, and you'll keep on going.
So any massive object can capture any smaller object -- if the conditions are right. ;-)