the apparent magnitude of star is how bright they look to us we are on the earth looking up into space which would look brighter

Small star

Big star

I think that is the big star
thank you in advance

Correct.

You're welcome! The apparent magnitude of a star refers to how bright it appears to an observer here on Earth. The brighter the star appears, the smaller its magnitude. So, in this case, if you're comparing a small star and a big star, the big star would generally appear brighter to us on Earth.

You're welcome! The apparent magnitude of a star refers to how bright it appears from Earth. Since you're comparing a small star to a big star, it is likely that the big star will appear brighter. However, to be sure, we can look at the scientific method astronomers use to measure the apparent magnitude of stars.

Astronomers use a scale called the Magnitude Scale to measure the brightness of stars. The scale originated with the ancient Greeks, who classified the brightest stars as magnitude 1 and the dimmest visible stars as magnitude 6. In this scale, smaller numbers represent brighter stars, and larger numbers represent dimmer stars.

To determine the apparent magnitude of a star, astronomers measure the amount of light they receive from the star and compare it to known reference stars. They use specialized instruments, such as photometers, to measure the star's brightness accurately.

In your case, if you have information about the apparent magnitudes of the small and big stars, you can compare their values. The star with the lower apparent magnitude will appear brighter from Earth. So, if the apparent magnitude of the big star is lower than that of the small star, then your initial assumption is correct, and the big star will indeed appear brighter.

However, please note that the apparent magnitude can also be influenced by factors such as the star's distance from Earth and the presence of any atmospheric conditions that might affect its visibility.