Question

The insolation—the Solar energy delivered to the surface of the Earth—is about 1 kW per square meter. This is the energy you feel when you are on the beach on a sunny day. What would be the insolation at Jupiter in those same units? What about at Pluto?

Problem 4: The insolation-the Solar energy delivered to the surface of the Earth-is about 1 kW per square meter. This is the energy you feel when you are on the beach on a sunny day. What would be the insolation at Jupiter in those same units? What about at Pluto?

Answer 1

Solution -

The solar constant at Earth is around 1,361 watts per square. That is the amount of radiation energy that hits the upper surface of the Earth’s atmosphere.

So, based on the fact that this energy lands on the surface area of a sphere = 4πr2

Sun -> Earth distance = 1.496 x 10^11 meters.

Sun -> Jupiter distance = 7.783 x 10^11 meters.

Jupiter is 5.203 times as far away as the Earth.

Square this value, 27.07, and then divide 1,361 by it = 50.333 watts/square meter.

Or another way of saying the same thing is that it is just over 27 times less intense than on Earth.

In the same way we can calculate for the Pluto - Perihelion -

Sun -> Earth distance = 1.496 x 10^11 meters.

Sun -> Pluto - Perihelion distance = 4.436 x 10^12 meters.

Pluto - Perihelion is 29.652 times as far away as the Earth.

Square this value, 879.26 , and then divide 1,361 by it = 646.04 watts/square meter.

In the same way we can calculate for the Pluto - Aphelion​​​​​​​ -

Sun -> Earth distance = 1.496 x 10^11 meters.

Sun -> Pluto - Perihelion​​​​​​​ distance = 7.736 x 10^12 meters.

Pluto - Perihelion is 49.30 times as far away as the Earth.

Square this value, 2430.96 , and then divide 1,361 by it = 1786.06 watts/square meter.

Note - The value of isolation is 1.361 KW / square meter which is the actual value of it but in question it was given that about 1 KW / square meter so for the sake of accurate results I have taken the actual value .

Please appreciate the efforts if you finds the answer valid and conceptually good.