Questions about Subsolar Temperature

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In summary, the equations for planetary subsolar temperature are derived from equating the object's luminosity with the product of absorbed flux from the star and the absorption area of the object. The first equation assumes that the absorbing and radiating areas are the same, while the second equation allows for a more general case where the absorbing area is B and the radiating area is C. The special case where B=C is applicable for a small subsolar patch, while for a rapidly rotating planet, C=4B and for a tidally locked planet, C=2B.
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MathIsFun
1. The problem statement, all variables, and given/known data
I'm having a little trouble understanding planetary subsolar temperatures. The first equation comes from viewing the absorbing and radiating areas of an object as the same and the second equation comes from viewing the absorbing area as [itex]B[/itex] and the radiating area as [itex]C[/itex].

Homework Equations


[tex]T_{ss}=\left(\frac{L\left(1-A\right)}{4\pi d^{2} \sigma}\right)^{\frac{1}{4}}[/tex] [tex]T=\left(\frac{BL\left(1-A\right)}{4\pi Cd^{2} \sigma}\right)^{\frac{1}{4}}[/tex]

[itex]L[/itex] is the luminosity of the star, [itex]A[/itex] is the bond albedo of the object, and [itex]d[/itex] is the star-object distance. These equations are derived from equating the luminosity of the object with the product of the absorbed flux from the star and the absorption area of the object.

The Attempt at a Solution


I understand that the second equation is a more general form, but how do you know when the special case applied in the first equation holds? I think this would require that the energy that is absorbed be retransmitted through the same area before it can be distributed throughout the object, but how can you tell when this will occur? Does the second equation give the subsolar temperature in a general case, or is subsolar temperature specifically when you take [itex]B=C[/itex]?

Thanks
 
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  • #2
From reading https://en.m.wikipedia.org/wiki/Effective_temperature, I gather that for a spherical planet, taken as a whole, B is πr2. If it is rapidly rotating then we take emission as being from the whole surface, so C=4πr2=4B. For a tidally locked planet the radiation is only from the lit half, so for that half C=2B. For a small subsolar patch B=C.
 

Related to Questions about Subsolar Temperature

1. What is subsolar temperature?

Subsolar temperature refers to the temperature at the point on a planet's surface directly facing the sun. This point is also known as the subsolar point.

2. How is subsolar temperature measured?

Subsolar temperature can be measured using instruments such as thermometers or infrared sensors. It is also possible to estimate subsolar temperature using mathematical models and data on solar radiation and planetary surface properties.

3. What factors affect subsolar temperature?

Subsolar temperature is primarily affected by the distance between the planet and the sun, the tilt of the planet's axis, and the composition and reflectivity of the planet's surface. Other factors such as atmospheric conditions and the rotation of the planet also play a role.

4. Why is subsolar temperature important to study?

Subsolar temperature is important to study because it can provide insights into the overall climate and weather patterns of a planet. It is also essential for understanding the habitability of a planet and its potential for supporting life.

5. How does subsolar temperature vary on different planets?

Subsolar temperature varies greatly among different planets, depending on their size, distance from the sun, and atmospheric conditions. For example, the subsolar temperature on Mercury can reach over 800 degrees Fahrenheit, while on Earth it ranges from -40 to 50 degrees Fahrenheit.

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