a way to tell if a star has planets is to observe a wobble in its position. i.e when a planet orbits a star it pulls at it making the star move slightly in its direction. when seen from far away it looks like the star is moving back and forth. This is a very rough explanation and can no doubt be improved upon.
There are many ways to determine this. Observing it directly, or collecting observations, over a long period of time can reveal an orbit. Periodic variation or non-linear variation in parameters such as parallax, proper motion or radial velocity can also reveal companions.
Binary stars do not determine anything to a star. There are simply a pair of stars which are sufficiently close to each other so as to form a pair bound in one another's gravitational grip.
Since a planet's light is reflected it appears to be steady (non twinkling). Star light twinkles.
SSo the astronomers can tell us what is happening to the sun. that good enough? :)
The center of the orbit is between them in proportion to their masses. But the mass of the sun is so much larger compared to the mass of the planets that to a casual observer they do revolve around the center of the sun. Because planets don't orbit the exact center of stars, astronomers can see stars that "wobble" and can tell they have planets orbiting them. They will also get an idea of the period of those planets' revolutions around the star.
How hot it is.
Ancient astronomers can tell the difference the same way you can tell now - the planets move, while the stars stay in the same patterns. The word "planet" comes from the Greek word for "wanderer". The 'planets' were the lights in the sky that moved. Originally the Greeks included the Sun and Moon as planets, because they were light's that moved through the sky. Also, the closer and bigger planets, Jupiter, Mars & Venus are also MUCH brighter than stars. The smaller planets and the ones that are far, far away (Mercury & Saturn) are also bright - but not much brighter than the brightest stars in the sky. They also all travel in the same narrow path in the sky - the ecliptic. It's the same path the sun & moon follow in the sky through the months & year. These 7 lights were visible in the sky without telescopes - Sun, Moon, Mars, Mercury, Jupiter, Venus & Saturn - which is how we got our 7 days of the week.
What elements the star is made of.
What makes up the star or element.
Because of perturbations within the observed star.
Because of perturbations within the observed star.
I'm not sure what you mean by "Star planets." However, I can tell you that there are 8 known planets that orbit the star Sol, including Earth (Sol 3).
The temperature of a star is determined for it's colour spectrum. The hotter the star the more the spectrum is towards blue where as a cooler star has a spectrum closer to red.
UV is studied in strength from stars like our sun. they use this to tell how old the other star is and how far it is from death
Since a planet's light is reflected it appears to be steady (non twinkling). Star light twinkles.
conclusion about binary tree
Precisely by the eclipse - that's what an "eclipsing binary system" is all about. The idea is that one of the stars partially (or completely, in some cases) covers the other star; with the result that the combined brightness (as seen from Earth) gets less for some time.
The collection of planets and their star (primary) are called a solar system. The planets themselves are called "exoplanets." Once we can tell they fit our definition of planet (having cleared their orbits, etc.) we would probably just refer to them as planets.
SSo the astronomers can tell us what is happening to the sun. that good enough? :)