Physics: Sirius is 22 times more luminous that the Sun, and Polaris is 2350 times more luminous that the Sun. Sirius appears 23 times brighter than Polaris. Polaris is times farther away than Sirius.

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Sirius is 22 times more luminous that the Sun, and - id228349968, TheOneWhoSucksAtMeth

Ответ:

josephmelichar777

05.02.2022

Physics

Polaris is approximately 4.796 times farther away than Sirius.

Explanation:

According to the inverse-square law, widely used in wave phenomena, the luminosity, a form of intensity of electromagnetic webs, is inversely proportional to the square of distance. In other words, we get the following definition:

$I \propto \frac{1}{r^{2}}$

$I = \frac{k}{r^{2}}$ (Eq. 1)

Where:

- Proportionality ratio, measured in watts.

- Distance from the center of the star, measured in meters.

- Luminosity of the star, measured in watts per square meter.

Then, we eliminate the proportionality ratio by constructing the following relationship:

$I_{S}\cdot r_{S}^{2} = I_{P}\cdot r_{P}^{2}$ (Eq. 2)

Where:

$I_{S}$ , $I_{P}$ - Intensities of Sirius and Polaris, measured in watts per square meter.

$r_{S}$ , $r_{P}$ - Distances from centers of Sirius and Polaris, measured in meters.

After some algebraic handling, we get that:

$\frac{r_{P}}{r_{S}} = \sqrt{\frac{I_{S}}{I_{P}} }$

If we know that $\frac{I_{S}}{I_{P}} = 23$ , then the distance ratio of Polaris to Sirius is:

$\frac{r_{P}}{r_{S}} =\sqrt{23}$

$\frac{r_{P}}{r_{S}} \approx 4.796$

In a nutshell, Polaris is approximately 4.796 times farther away than Sirius.

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Sirius is 22 times more luminous that the Sun, and Polaris is 2350 times more luminous that the Sun. Sirius appears 23 times brighter than Polaris. Polaris is times farther away than Sirius.

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