Question

The star named Capella has an apparent magnitude of 0 while the star named Polaris has an apparent magnitude of 2, which means that Capella appears ________ Polaris in the night sky.

Answer 1

Capella, with an apparent magnitude of 0, appears brighter than Polaris, which has an apparent magnitude of 2. Apparent magnitude is a scale where lower numbers indicate brighter stars. Polaris is also known as the North Star and is close to the north celestial pole.

Step-by-step explanation:

The star named Capella has an apparent magnitude of 0 while the star named Polaris has an apparent magnitude of 2, which means that Capella appears brighter than Polaris in the night sky.

In the system of apparent magnitudes, lower or negative numbers indicate brighter stars. Therefore, a star with an apparent magnitude of 0, like Capella, will appear brighter in the sky compared to Polaris, which has an apparent magnitude of 2. It's interesting to note that Polaris is also referred to as the North Star or pole star, and it plays a significant role in navigation due to its position close to the north celestial pole.

While Polaris is often mistaken for the brightest star, that title actually belongs to Sirius, with an apparent magnitude of -1.5.

Answer 2

Brighter than

Step-by-step explanation:

m₁ = Apparent magnitude of Capella = 0

m₂ = Apparent magnitude of Polaris = 2

L₁ = Brightness of Capella

L₂ = Brightness of Polaris

From Pogson's ratio

`m_1-m_2=-2.5log_(10) (L_1)/(L_2)\\\RIghtarrow 0-2=-2.5log_(10) (L_1)/(L_2)\\\Rightarrow (-2)/(-2.5)=log_(10) (L_1)/(L_2)\\\Rightarrow 0.08=log_(10) (L_1)/(L_2)\\\Rightarrow 10^(0.08)=(L_1)/(L_2)\\\Rightarrow 1.202=(L_1)/(L_2)\\\Rightarrow L_1=1.202\ L_2`

∴ The brightness of Capella is 1.202 times the brightness of Polaris