whats the differences in magnitudes of the sun and sirius?
Since your question title deals with apparent magnitudes, I will assume that is the type for which you want the difference between sun and Sirius (the apparent-brightest star other than the sun). The sun's apparent brightness is much higher, and its apparent magnitude accordingly much lower, than Sirius becasue it is so much closer. Lower magnitude numbers correspond to higher brightness, because of some convention adopted centuries ago.
The sun's apparent magnitude is -26.7 and that of Sirius is -1.5. That difference of nearly 25 magnitudes corresponds to a factor of 10^10 in received radiation, since each 5 magnitudes is a factor of 100.
To find the differences in magnitudes between the Sun and Sirius, we need to understand that magnitude is a measure of the brightness of celestial objects. The lower the magnitude value, the brighter the object appears.
To get the specific magnitudes of the Sun and Sirius, we can refer to astronomical catalogs or databases. The magnitude of the Sun is quite challenging to measure as it is excessively bright compared to other stars. However, if we consider the Sun's apparent magnitude (as seen from Earth), it is approximately -26.74.
Sirius, on the other hand, is the brightest star in the night sky. Its apparent magnitude is around -1.46, which makes it significantly brighter than the Sun when observed from Earth.
To summarize, the difference in magnitudes between the Sun and Sirius is approximately 25.28, with Sirius having a lower magnitude value and therefore appearing brighter in the night sky.