The energy output of a star is given by the Stefan-Boltzmann Law:

$L = \sigma T^4$

where:

• $L$ is the luminosity (energy output),
• $\sigma$ is the Stefan-Boltzmann constant,
• $T$ is the temperature of the star.

If star A has 2.91 times the temperature of star B, then the ratio of their luminosities is:

$\frac{L_A}{L_B} = \left(\frac{T_A}{T_B}\right)^4$

Substituting $T_A / T_B = 2.91$:

$\frac{L_A}{L_B} = (2.91)^4$

Calculating:

$(2.91)^4 = 71.46$

Thus, star A is outputting 71.46 times more energy than star B.

Final Answer: 71.46

Would you like a more detailed breakdown?

Here are some related questions you might find interesting:

1. How does the Stefan-Boltzmann Law affect different types of stars?
2. What role does surface area play in a star’s luminosity?
3. If a star’s radius increases, how does its luminosity change?
4. What is the relationship between a star’s color and its temperature?
5. How does the luminosity of a star affect its lifespan?

Tip: The Stefan-Boltzmann Law shows why hotter stars are significantly brighter than cooler ones, even if they have the same size! 🚀