For your question 1 and 3, you need some background knowledge to make sense of any answer. So here we go: The calculation of the age of the universe, the determination of the composition of the very far objects like stars and galaxies, the measurement of distance to very far stars, and measurement of the speed with which a very far star is approaching and receeding from us are intricately related.
1. The composition of the atmosphere of a star, gases in galaxies, and such can be determined by looking for unique patterns of bands of light or darkness in the spectrum of their light. This pattern is called obsorption lines. What element makes what absorption patterns is easy to determine in the laboratory.
2. How fast a star is approaching and receeding from us can be determined by looking at how far the particular patterns of obsorption lines is displaced from their normal position in the electro-magnetic spectrum, which can be determined easily in the laboratory. The displacement of the obsorption lines exhibits a property called doppler effect. Obsorption lines of objects receeding from us shifts to the red side of spectrum, those of objects approaching us shifts to the blue side. For simplicity let's call them, as astronomers do, red shift and blue shift. The greater the red shift, the faster the recession.
3. How far any arbitray isolated star is from us is normally hard to determine, but when particular type of star explodes the distance to the explosion is easy to determine. This type of explosion is called type I super nova, and all type I super nova falls within an very narrow range of brightness. Type I super nova is thus called a "standard candle". If you know how bright a candle is close up, and you can measure how bright it appears to you from the distance, you can immediately determine what that distance is. Similarly if you see a type I super nova exploding, and you can measure its brightness as seen by you, then you know how far it is. Most stars occur in galaxies. So if you see a type I super nova exploding inside a galaxy, you know how far that galaxy is from us, and hence how far all the stars of that galaxy is from us.That is useful information. Can you please suggest me a good book on the subject to study more about it?
Quote:Now when the earth, or indeed the whole solar system, was first forming, we have powerful reasons to believe many types of minerals containing radioactive elements have had any previously accummulated resultant elements purged. Thus for these minerals their radioactive clock was reset to zero. By measuring how much the radioactive clock has run since, we know how old the earth, the moon, etc, is. The best estimate of the age of the earth currently is 4.56 billion years.
