Question

Betelgeuse is roughly the same temperature as Proxima Centauri, the closest star to the Earth aside from the Sun. However, it is $10^{9}$ times brighter. How much larger in radius is Betelgeuse than Proxima Centauri?

Name: Problem 6, Chapter 57: Pathways to Astronomy
Uploaded: 2021-04-02T03:00:09-08:00
Duration: 2 min 18 s
Channel: Ajay Singhal
Description: Betelgeuse is roughly the same temperature as Proxima Centauri, the closest star to the Earth aside from the Sun. However, it is 10^9 times brighter. How much larger in radius is Betelgeuse than Proxima Centauri?

   Betelgeuse is roughly the same temperature as Proxima Centauri, the closest star to the Earth aside from the Sun. However, it is $10^{9}$ times brighter. How much larger in radius is Betelgeuse than Proxima Centauri?

Pathways to Astronomy

Stephen E. Schneider 2nd Edition

Chapter 57, Problem 6

Instant Answer

Solved by Expert Ajay Singhal

04/02/2021

Step 1

Step 1: Recall the formula for the luminosity of a star, which is given by: L = 4πR²σT⁴ where L is the luminosity, R is the radius, σ is the Stefan-Boltzmann constant, and T is the temperature. Show more…

Show all steps

Thanks for your feedback!

Betelgeuse is roughly the same temperature as Proxima Centauri, the closest star to the Earth aside from the Sun. However, it is $10^{9}$ times brighter. How much larger in radius is Betelgeuse than Proxima Centauri?

Play audio

Feedback

Ajay Singhal and 53 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Stefan-Boltzmann Law

The Stefan-Boltzmann law is a fundamental principle in astrophysics, stating that the power radiated per unit surface area of a black body is directly proportional to the fourth power of its absolute temperature. This law enables the calculation of a star’s luminosity in terms of its radius and temperature, providing the essential link between the energy output and the physical dimensions of stars.

Luminosity-Radius-Temperature Relationship

The relationship between a star's luminosity, radius, and temperature is encapsulated in the formula L ? R²T?. When the temperatures of two stars are the same, this relationship simplifies so that the luminosity is directly proportional to the square of the radius. This means that a star that is a billion times more luminous than another with the same temperature must have a radius that is the square root of a billion (i.e., 10^(4.5) or about 31,622 times) larger.

Please give Ace some feedback