Yes, it is possible today.
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There are billions of galaxies, and you haven't mentioned which one you're
interested in.
If you mean the Milky Way galaxy ... the one of which the Sun is a member ...
then the task is easily begun without any telescope at all.
ALL of the stars you see with your eyes when you stand in your back yard
and browse the night-time sky are stars in the Milky Way galaxy.
Spotting individual stars in OTHER galaxies does require a telescope.
Unless you have a extremely powerful telescope, a galaxy and a star look almost the same.
Through the Spitzer Telescope
be quit @$$ #**()
You can see more stars than with just the naked eye
Sees stuff. STARS!
infrared
Astronomers refer to a galaxy with a jumbled scattering of stars as an "irregular galaxy." These galaxies lack a defined shape or structure, distinguishing them from spiral or elliptical galaxies. Irregular galaxies often contain young stars, gas, and dust, and they can be the result of gravitational interactions or collisions with other galaxies.
Launched on April 24th 1990 the purpose of the Hubble space telescope is so astronauts and astronomers and even the public can discover new images of our Galaxy and other Galaxy's and other planets
Astronomers study stars in many different places but typically, they study in observatories. The buildings where there is a telescope
Well a telescope can be used just about anywhere but it is most commonly used by astronomers and astrocartographers(People who study and take pictures of the sun,moon and stars)
Collectively they are called Astronomers and Astrophysicists. Either professionals or amateurs.There are many types of astronomers, defined by how they study the stars. The most well-known are those that use optical telescopes followed closely by those that use Radio-telescope to pick up wavelengths other than visible light. there are many others and many other ways to collect data on the galaxies and stars.Astrophysicists are astronomers and may also collect direct data, yet they are more interested in the working behind the data. They deal in physics and theories of the galaxies.
The galaxy was named after milk because when early astronomers looked at the sky they noticed a band of stars that somewhat looked like milk!