The formula to calculate the black hole mass (BHM) is:
\[ BHM = \frac{R}{3} \]
Where:
Let's say the radius of the event horizon (\( R \)) is 9000 km. Using the formula:
\[ BHM = \frac{9000}{3} \]
We get:
\[ BHM = 3000 \]
So, the black hole mass (\( BHM \)) is 3000 solar mass units.
The black hole mass is the mass of a black hole, typically measured in solar mass units. It can be estimated using the radius of the event horizon, which is the boundary beyond which nothing, not even light, can escape the gravitational pull of the black hole.
Definition: This formula calculates the mass of a black hole based on the radius of its event horizon.
Formula: \( M = \frac{R \cdot c^2}{2 \cdot G} \)
Example: \( M = \frac{10 \cdot (3 \times 10^8)^2}{2 \cdot 6.674 \times 10^{-11}} \)
Definition: This equation calculates the mass of a black hole using the orbital velocity and radius of an orbiting object.
Formula: \( M = \frac{r \cdot v^2}{G} \)
Example: \( M = \frac{1 \times 10^6 \cdot (2 \times 10^5)^2}{6.674 \times 10^{-11}} \)
Definition: This calculator helps determine the size of a black hole based on its mass.
Formula: \( R = \frac{2 \cdot G \cdot M}{c^2} \)
Example: \( R = \frac{2 \cdot 6.674 \times 10^{-11} \cdot 5 \times 10^{30}}{(3 \times 10^8)^2} \)
Definition: This calculator estimates the lifetime of a black hole based on its mass.
Formula: \( t = \frac{5120 \cdot \pi \cdot G^2 \cdot M^3}{\hbar \cdot c^4} \)
Example: \( t = \frac{5120 \cdot \pi \cdot (6.674 \times 10^{-11})^2 \cdot (1 \times 10^{30})^3}{1.054 \times 10^{-34} \cdot (3 \times 10^8)^4} \)
