Ch. 44 - Astrophysics and Cosmology

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 44 - Astrophysics and Cosmology

Problem 6

Chapter 39, Problem 6

We saw earlier (Chapter 19) that the rate energy reaches the Earth from the Sun (the “solar constant”) is about 1.3 x 10³ W/m². What is (a) the apparent brightness b of the Sun, and (b) the intrinsic luminosity L of the Sun?

Verified step by step guidance

Step 1: Understand the problem. The apparent brightness (b) is the power per unit area received from the Sun at the Earth's distance. The intrinsic luminosity (L) is the total power output of the Sun, which can be calculated using the relationship between brightness, luminosity, and distance.

Step 2: Recall the formula for apparent brightness:

b = L / (4 π d

²), where

b

is the apparent brightness,

L

is the luminosity, and

d

is the distance from the Sun to the Earth.

Step 3: Use the given solar constant, which is the apparent brightness at the Earth's distance,

b = 1.3 × 10

³ W/m². The distance from the Earth to the Sun is approximately

d = 1.496 × 10

¹¹ m.

Step 4: Rearrange the formula for luminosity:

L = b × 4 π d

². Substitute the known values of

b

and

d

into this equation to calculate the Sun's intrinsic luminosity.

Step 5: Perform the calculation to find

L

. Ensure that the units are consistent throughout the calculation, and express the final result in watts (W).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Solar Constant

The solar constant is the amount of solar energy received per unit area at a distance of one astronomical unit (AU) from the Sun, approximately 1.3 x 10³ W/m². This value represents the average energy output from the Sun that reaches the outer atmosphere of Earth, providing a baseline for understanding solar energy and its effects on our planet.

Apparent Brightness

Apparent brightness refers to the amount of light received from a celestial object, such as the Sun, as observed from a specific distance. It is influenced by the object's intrinsic luminosity and the distance from the observer, following the inverse square law, which states that brightness decreases with the square of the distance from the source.

Intrinsic Luminosity

Intrinsic luminosity is the total amount of energy emitted by a star or celestial body per unit time, regardless of its distance from the observer. It is a fundamental property of stars, allowing astronomers to compare their true energy output, and is crucial for understanding stellar evolution and the physical characteristics of stars like the Sun.