Effect of Earth-Sun Distance Variance on Effective Temperature

In summary, the distance between the Sun and Earth varies throughout the year, with a minimum in January and a 3.3% increase in July. This affects the effective temperature of the Earth, with the corresponding change in the solar flux, which can be calculated using the effective temperature equation and the solar constant equation.
  • #1
il27

Homework Statement



The distance between the Sun and the Earth varies during the year: it is a minimum in January, and about 3.3% larger at its maximum in July. What is the corresponding change in the Earth's effective temperature?

Homework Equations



Energy absorbed: $$ E_{abs} = \pi R^2 (1- \alpha) F_0 $$
energy emitted: $$ E_{emit} = 4 \pi R^2 \sigma (T_E)^4 $$

The Attempt at a Solution



I tried finding the effective temperature equation:

The effective temperature equation:

$$ T_E^4 = \frac{(1 - \alpha) F_0}{4 \sigma} $$

but I am stuck on how to account for the changing distances between the sun and the earth.
Please help, thank you!
 
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  • #2
F0, the flux of solar radiation at the Earth, is dependent on the distance between the Earth and the Sun. Do you know how much F0 changes if the Earth-Sun distance doubles, for example?
 
  • #3
phyzguy said:
F0, the flux of solar radiation at the Earth, is dependent on the distance between the Earth and the Sun. Do you know how much F0 changes if the Earth-Sun distance doubles, for example?

Oh okay. the solar constant would decrease right?
what is the equation to find the solar contsant where it relies on the distance between the sun and the earth?
 
  • #4
help
 
  • #5
i think i understand the equation. i use the effective temperature equation but find two different solar constant values.
however, what does it mean when it is a minimum in January, and about 3.3% larger at its maximum in July?
is the minimum the distance between the sun and the earth? while 3.3% larger than that is 3.3% added to the distance?
 
  • #6
il27 said:
i think i understand the equation. i use the effective temperature equation but find two different solar constant values.
however, what does it mean when it is a minimum in January, and about 3.3% larger at its maximum in July?
is the minimum the distance between the sun and the earth? while 3.3% larger than that is 3.3% added to the distance?

Yes. Whatever the distance is in January, it is 3.3% larger in July. When the distance increases by 3.3%, how much does the solar flux decrease?
 

FAQ: Effect of Earth-Sun Distance Variance on Effective Temperature

What causes the Earth and Sun's variance?

The Earth and Sun's variance is caused by the Earth's orbit around the Sun. The Earth's orbit is not a perfect circle, but rather an elliptical shape. This means that at certain points in its orbit, the Earth is closer or further away from the Sun, causing differences in the amount of sunlight and heat that reaches the Earth's surface.

How does the Earth and Sun's variance affect our seasons?

The Earth and Sun's variance plays a significant role in the changing of seasons. When the Earth is closer to the Sun, it receives more direct sunlight and experiences warmer temperatures, resulting in summer. When the Earth is further away, it receives less direct sunlight and experiences cooler temperatures, resulting in winter.

Is the Earth and Sun's variance constant?

No, the Earth and Sun's variance is not constant. The Earth's orbit is affected by other factors such as the gravitational pull of other planets and the tilt of the Earth's axis. This can cause slight variations in the Earth's distance from the Sun, resulting in changes in the amount of sunlight and heat that reaches the Earth's surface.

How does the Earth and Sun's variance impact climate change?

The Earth and Sun's variance is not the main cause of climate change, but it can have an impact on it. Changes in the Earth's orbit and distance from the Sun can affect the distribution of sunlight and heat on Earth, potentially contributing to changes in temperature and weather patterns.

Can we predict the Earth and Sun's variance?

Yes, scientists can predict the Earth and Sun's variance using mathematical models and data analysis. By studying past patterns and changes in the Earth's orbit and the Sun's activity, scientists can make predictions about future variations and how they may impact our planet. However, these predictions are not always exact and can be influenced by many factors.

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