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?

검증된 단계별 안내

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).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.