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Consider two stars: our Sun and a nearby star called Star C. The Sun has a radius of 1 solar radius (1 Rsun), and a temperature of 5,800 K. Star C has a radius of 0.01 Rsun) and a temperature of 10,000 K. Which star is more luminous? How many times more luminous is it? Show your work below.

Consider two stars: our Sun and a nearby star called Star C. The Sun has a radius of 1 solar radius (1 Rsun), and a temperature of 5,800 K. Star C has a radius of 0.01 Rsun) and a temperature of 10,000 K. Which star is more luminous? How many times more luminous is it? Show your work below.

Applications and Investigations in Earth Science (9th Edition)
Applications and Investigations in Earth Science (9th Edition)
9th Edition
ISBN:9780134746241
Author:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
Publisher:Edward J. Tarbuck, Frederick K. Lutgens, Dennis G. Tasa
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**Problem 13** Consider two stars: our Sun and a nearby star called Star C. The Sun has a radius of 1 solar radius (\(1 \, R_{\text{Sun}}\)), and a temperature of 5,800 K. Star C has a radius of 0.01 \(R_{\text{Sun}}\), and a temperature of 10,000 K. Which star is more luminous? How many times more luminous is it? Show your work below.
Transcribed Image Text:**Problem 13** Consider two stars: our Sun and a nearby star called Star C. The Sun has a radius of 1 solar radius (\(1 \, R_{\text{Sun}}\)), and a temperature of 5,800 K. Star C has a radius of 0.01 \(R_{\text{Sun}}\), and a temperature of 10,000 K. Which star is more luminous? How many times more luminous is it? Show your work below.
**Basic Stellar Properties** Every star has certain properties that help to define it. Some of the main properties of stars are: | **Surface Temperature:** | The amount of heat on the surface of a star | |--------------------------|---------------------------------------------| | **Luminosity:** | The amount of energy a star gives off each second | | **Radius:** | The size of a star; specifically, the distance between the center and surface of the star | | **Mass:** | The amount of material in a star | The luminosity of a star is related to its temperature and radius. Hotter stars are more luminous (give off more light) than cooler stars of the same size. Similarly, if two stars are at the same temperature, the larger star will be more luminous. The mathematical formula that describes how these properties are related is: \[ L \propto T^4 R^2 \] \[ \text{Luminosity} \propto (\text{Temperature})^4 \times (\text{Radius})^2 \] Let’s do an example to understand what this proportionality means.
Transcribed Image Text:**Basic Stellar Properties** Every star has certain properties that help to define it. Some of the main properties of stars are: | **Surface Temperature:** | The amount of heat on the surface of a star | |--------------------------|---------------------------------------------| | **Luminosity:** | The amount of energy a star gives off each second | | **Radius:** | The size of a star; specifically, the distance between the center and surface of the star | | **Mass:** | The amount of material in a star | The luminosity of a star is related to its temperature and radius. Hotter stars are more luminous (give off more light) than cooler stars of the same size. Similarly, if two stars are at the same temperature, the larger star will be more luminous. The mathematical formula that describes how these properties are related is: \[ L \propto T^4 R^2 \] \[ \text{Luminosity} \propto (\text{Temperature})^4 \times (\text{Radius})^2 \] Let’s do an example to understand what this proportionality means.
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