Question
How to calculate the Polaris star radius with answer
Answers
GPT 3.5
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.
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.