where G is a gravitational constant. If we can measure speed and size of orbit, we can estimate the mass of the central object. For our sun it is about
Most solar systems are elliptical rather than circular. The principle's the same, but the arithmetic is harder!
Cosmological models predict a definite relation between speed and distance; for nearby objects, distance is proportional to speed. This makes it straightforward to decide the distance of say a galaxy.
For objects which are not too far away (and not too small) the difference in angular direction between one boundary and another is directly proportional to its size:
which is called a light year.
If we see light coming from a distant source one million light years away, we are seeing the object not as it is now, but how it was one million years ago.
The same effect happens with light. If a star is approaching us it appears bluer, and if it is receding it appears redder. The shift in frequency, usually called the redshift, is proportional to the speed at which it is moving away from us.
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