How do we know that elements that are on earth are also in the sun?

Answer 1

Spectroscopy is correct.

When an atom of matter gets "excited", one (or many) electrons gather the energy and get to a higher orbit. When the electron "falls back" to its lowest possible orbit (called the "ground state") it will let out a photon with a very precise frequency. The exact frequency depends on the state of the electron's orbit before the fall. Each possible electron orbit has a very precise energy level (there are no in-between).

Each different element has different ground states for each electron orbits. In a lab, it is possible to establish, for a given element, the possible photon wavelengths that can be emitted by electrons falling from a high-energy level to a low energy level. The collection of these wavelengths forms the "emission lines" of that element.

The most famous emission lines are those of hydrogen (most common element in the universe, including in stars). The different patterns, from hydrogen, are called by the names of the scientist who studied them (Balmer series, Lyman series, Paschen series...).

Also, objects that emit light of all frequencies (like a star) will see some of its light energy absorbed by atoms. The photons of the very same frequency are absorbed by the electrons as they "climb" from the ground state. Thus, the sun's spectrum has "absorption lines" that cover the same wavelengths as the emission lines of the atoms in the Sun's atmosphere.

So, when we study the light from ths sun, the missing wavelengths tell us what atoms are absorbing the light in the sun's atmosphere. When there is a total eclipse, blocking the light from the sun, we can see the spectrum of the emission lines from the gas in the corona and identify the elements in the corona.

The element Helium was first identified by its lines in the Sun's spectra (the name helium is from "Helios", Greek god of the Sun).

PS:
I just found my copy of "Lange's Handbook of Chemistry" (by John Dean. McGraw-Hill, 1992). Section 7 is called Spectroscopy. It includes tables of "Sensitive Lines" which are the wavelengths emitted by elements (and some molecules) under various lab conditions (e.g., when in a flame, when ionized, single bonds versus double bonds).
The section covers 139 pages and is designed so that a chemist can identify a compound by measuring the wavelengths of its emission lines.

By looking at a pattern, one can identify an element (usually hydrogen). Then by measuring the observed wavelengths and comparing with the wavelengths obtained in a lab, one can measure the radial speed of the star by calculating the difference between the observed wavelengths and the lab wavelengths.

Answer 2

We built the Genesis spacecraft in 1995 I believe to capture solar winds and rays which would contain particles of the elements the sun's gases, radiation, etc. are comprised of. Specialized solar panels collected the particles as the craft orbited the poles (distantly!) of the sun.

We tried to use helicopters flown by Hollywood stunt men to retrieve Genesis when it re entered Earth's atmosphere in the troposphere, but the parachute on the capsule failed to eject and it crashed into Utah's dusty ground.

However, we were able to distinguish the surfacial Utah dust particles from the solar samples, fortunately!

Thus, we have extensive knowledge of the sun's composition thanks to the Genesis mission.

(PS- the panels were designed to be especially sensitive to diamond, sapphire, silicon and gold)

Answer 3

Spectroscopy

Answer 4

We detect their spectra