How does the distance of a star can be calculated by an amateur astronomer ? How has it been done in the ancient time?
Measuring distances to celestial objects is one of the hardest problems in astronomy. Even scientists sometimes have trouble figuring out how far are the objects they study!
Since we totally lack depth perception when we look at the night sky, it is impossible to tell the distance to stars just by looking at them. In fact, ancient astronomers thought that all stars were positioned at the same distance from Earth on a large hollow sphere. Only with telescopes can we start to measure distances to nearby stars. The method used is called stellar parallax.
To get a feeling of what parallax is, put your hand in front of you, and then look at it with one eye at the time. You will notice that the position of your hand with respect to the background changes. The same trick is used to measure distances to stars. To do parallax, one needs to measure to position of a star with respect to background stars at an interval of 6 months (because 6 months is the largest distance you will get between two positions of the Earth on its orbit around the Sun). Then the parallax is the angle made by the two positions measured for the star you are interested in. These angles are very small, only small fractions of degrees in the sky, much less that you can resolve with your eye.
So unfortunately, the answer to your question is that you will not be able to measure distances to stars, unless you could have access to a telescope at a professional observatory, in which case it is still very hard to do.
This page updated on June 27, 2015