Theoretical vs. Actual Temperature in our Solar System

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  • 0:01 The Thermal Equilibrium
  • 1:45 The Solar Constant
  • 3:52 What Is Albedo?
  • 6:11 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

This lesson will go over the predicted vs. observed temperature of major celestial bodies in our solar system, if there's a discrepancy between them, and why.

The Thermal Equilibrium

Have you ever wondered why a blacktop is hot on a sunny day? That blacktop, like a sponge with water, absorbs solar energy. But it can't hold on to this solar energy for long and thus radiates it away. Like the blacktop on Earth, if a celestial body absorbs solar energy faster than it can get rid of it, it gets hotter. As it gets hotter, the rate at which it radiates energy increases.

If the celestial body radiates energy away faster than it can absorb it, it obviously gets cooler. As it gets cooler, the rate at which it radiates energy decreases. There's nothing too difficult to understand here. But there is one key thing. As an object gets hotter and hotter, its temperature will eventually stop rising because at a certain point it becomes hot enough to emit energy at the same rate at which it absorbs it.

As an object gets cooler and cooler, it will radiate more energy than it absorbs. It will eventually get cold enough, such that the rate at which it radiates energy away falls to the same rate at which it absorbs the solar energy. In either case, both situations are a kind of thermal equilibrium, a scenario where the temperature of a body stays constant since the rate at which it emits and absorbs energy is the same.

However, solar system bodies that have internal sources of heat will be hotter than we'd predict had they been heated by sunlight alone. Nevertheless, the temperature of a body that is also heated by internal sources is one where the rate at which energy that is radiated away is equal to the energy coming from internal sources plus that being absorbed from solar energy.

The Solar Constant

Other than the sun itself, we can estimate the temperatures of the celestial bodies in our solar system by pretending they are blackbodies that are in thermal equilibrium. A blackbody is a hypothetical and idealized object, one that is a perfect absorber of all wavelengths of radiation that fall on it.

This way, the temperature of such a celestial object will only depend on the distance away it is from the sun. You can imagine that our sun is just a ginormous heat lamp. As you travel away from a heat lamp, you know it's going to get colder. But this relationship isn't linear. Meaning, just because you are twice as far away from the sun, that doesn't mean it's twice as cold.

To understand why, we need to define the solar constant, which is the amount of solar energy hitting one square meter just above Earth's atmosphere every second. The solar constant is equal to about 1360 watts per square meter (1,360 joules per second per square meter).

At distances farther or closer to the sun that Earth, the brightness of solar radiation changes by an amount equal to the solar constant divided by the square of the distance from the sun in astronomical units. All of this complicated-sounding stuff really boils down to what you already know. The rate at which a solar system body can absorb warmth giving sunlight falls with increasing distance from the sun because the brightness of sunlight falls with increasing distance from the sun.

This means a planet like Mercury, much closer to the sun than Uranus, is receiving a lot of really bright sunlight. Consequently, it absorbs solar energy at a much higher rate than Uranus. In turn, this tells us that is has to balance this rate of absorption with a much higher rate of emission of radiation. Based on the first section, you know that a celestial body can only emit radiation at such a high rate if it has a high temperature.

What Is Albedo?

Because each solar system body isn't a true blackbody, it doesn't emit nor absorb radiation with perfect efficiency. This means that when calculating the expected temperature of a planet we must take albedo into consideration.

Albedo is the fraction of light that's reflected by a body. So, for a perfectly white object, the albedo is 1 and for a perfectly black object or surface, the albedo is 0. Snow and ice will be closer to 1 since they reflect a lot of sunlight and a blacktop will be closer to 0 since it reflects much less sunlight.

Similarly, each planet has a different albedo which contributes to its true temperature. Mercury has an albedo of almost 0.07. This means it absorbs 93% of light that hits it, whereas Venus has an albedo of 0.90, which means it's a lot more reflective than Mercury.

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