How to calculate the Polaris star radius with answer
There are several ways to calculate the Polaris star's radius, but one common approach is to use the Stefan-Boltzmann law.
The Stefan-Boltzmann law relates the luminosity (L) of a star to its radius (R) and temperature (T) by the equation: L = 4πR^2σT^4, where σ is the Stefan-Boltzmann constant.
To calculate the Polaris star's radius, we need to know its luminosity and temperature. The luminosity of Polaris is approximately 3,500 times that of our Sun, L = 3,500*Lsun. The temperature of Polaris is estimated to be around 6,000 Kelvin, T = 6,000 K.
Now let's plug these values into the Stefan-Boltzmann equation:
3,500*Lsun = 4πR^2 * σ * (6,000 K)^4
To make calculations easier, we can convert the solar luminosity to the SI unit (Watts). 1 Lsun is equal to 3.828 x 10^26 Watts.
3,500 * 3.828 x 10^26 = 4 * π * R^2 * (5.673 x 10^(-8)) * (6,000^4)
Let's simplify the equation:
1.340 x 10^30 = 1.5154 x 10^(-7) * R^2 * 1.296 x 10^21
Dividing both sides of the equation by (1.5154 x 10^(-7) * 1.296 x 10^21), we get:
R^2 = (1.340 x 10^30) / (1.5154 x 10^(-7) * 1.296 x 10^21)
R^2 = 8.2923 x 10^(1+30+7-(-21))
R^2 = 8.2923 x 10^(59)
Taking the square root of both sides of the equation, we find:
R ≈ 9.105 x 10^(59/2)
R ≈ 9.105 x 10^29
Therefore, the approximate radius of the Polaris star is 9.105 x 10^29 meters.