How are Planetary Energy Balance and Temperature Calculated?

Scientists are fascinated with things like the hotness or coldness of the surface of our planet. The interesting thing is that you do not need to be a theoretical physicist before you can do this calculation using basic math and physics. You can also do a correct calculation of the expected temperature of this planet right from the comfort of your room. 

The reference is being made to the expected temperature because the other factors like the effects of the oceans or atmosphere on the average planetary temperature have to be considered. It is now apparent that these factors influence the temperature of the planet so they have to be considered. That said, our assumption will be for a planet that has no water or air which can influence the calculation. 

Visible light coming from the Sun is loaded with energy which it releases on the planets in our Solar System. When this sunlight lands on our planet, it is absorbed. Any substance that has a temperature that is higher than the absolute zero releases electromagnetic radiation. When it has to do with the planets, the electromagnetic radiation being emitted is in the form of infrared radiation. The planet is going to continue on the path of warmth until the infrared energy is at equilibrium with the energy from the Sun. this is what the scientists referred to as the ‘thermal equilibrium’. With some fundamental physics, practically anyone can do the calculation for the temperature during which the point of thermal equilibrium is achieved. 

Satellites in space have been able to measure the quantity of energy landing on the planet in the form of sunlight. Even though the quantity differs with time, the average comes to around 1,361 watts of power for every square meter and that is quite significant. Scientists call this insolation and on earth, the value is 1,361W/m2 and it is also referred to as the solar constant. 

Before the amount of energy reaching the planet can be calculated, it is important to first identify the zone that is lit. This is then multiplied by the insolation (which is the unit of energy flow per unit area) to get the total amount of the incoming energy. 

The calculation of the area can be made a lot simpler by realizing that the amount of light captured by our planet is the same as the one blocked by a flat disc that has an equal diameter with the earth. As the area of any circle is the pi multiplied by the radius of the circle squared, which will be an easy one. For the sake of the calculation we are doing, the radius of the planet is approximately 6,371 kilometers (about 3,959 miles) on average. This is then multiplied by the quantity of energy for every unit area; this is going to give us the total amount of all the energy that the planet intercepts. 

So the formula is going to be something like this: 

Total energy intercepted = Solar constant (solar insolation) X Pi X radius of the Earth (squared)

A quick calculation here using the values gives us an incredible value of almost 174 petawatts of energy from the Sun – that is stunning indeed!

E = 1361 X 3.1416 X (6,371,000)2

E = 173.5 X 1015 watts

But since our planet is not black, a portion of this energy is not absorbed so it is reflected in space. This reflected energy is called albedo and a planet that is covered with ice or snow is said to have an albedo of almost 100%. On the other hand, a black planet has an albedo that is almost zero. 

To do determination of the quantity of energy that has been absorbed from the sun, the energy intercepted as calculated in the section above has to be multiplied then minus the albedo value. Hence the formula for the total energy absorbed will look like this: 

Energy absorbed = Solar constant X (1- albedo) X Pi X radius of the earth squared

History shows that even though we can do these calculations today in a matter of seconds owing to advanced technology, some scientists were the forerunners. In the 19th century, two scientists were able to calculate that the quantity of radiation released from an object will depend on the temperature of the substance. This is known as the Stefan-Boltzmann law in physics and it was arrived at by Joseph Stefan and Ludwig Boltzmann. 


As you can see, calculating the energy values of our planet is a lot easier than many think. This is because many of the constants to be used have already been worked out by scientists. All that is to be done is to insert the right values and this opens a new vista of understanding about this amazing planet we call home. 

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