Question

Solar constant for the earth is $2cal{\min ^{ - 1}}c{m^2}$. If the distance of mercury from the sun is 0.4 times than distance of the earth from the sun then the solar constant for mercury will be:

Answer 1

Hint: In this question, we will use the direct formula of solar constant. Further, by putting the given values in the formula, we will get our required result. Also, we will discuss the basics of the solar system and our Earth’s structure, for our better understanding.
Formula used:
$S \propto \dfrac{1}{{{r^2}}}$

Complete step by step solution:
As we know, the solar constant is inversely proportional to square of the distance from the Sun. here, it can be written as:
$\dfrac{{{S_{earth}}}}{{{S_{mercury}}}} = \dfrac{{r_{_{mercury}}^2}}{{r_{earth}^2}}$
Now, by substituting the given values in the above equation, we get:
$\dfrac{2}{{{S_{mercury}}}} = {\left( {0.4} \right)^2}$
Further solving:
$ \Rightarrow {S_{mercury}} = \dfrac{2}{{0.16}}$
$ \Rightarrow {S_{mercury}} = \dfrac{{200}}{{16}}$
$\therefore {S_{mercury}} = 12.5cal{\min ^{ - 1}}c{m^2}$
Therefore, we get the required result of the solar constant of mercury, which is given by the above value.

Additional information:
As we know that the solar system consists of stars, the Sun, and everything bound to it by the force of gravity , that are: the planets- Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune, also dwarf planets such as Pluto, dozens of moons and millions of asteroids, comets and meteoroids.
Here, we should also know the structure of our earth. We can say that the structure of the earth is divided into four major components called- the crust, the mantle, the outer core, and the inner core. Each of these layers has a unique chemical composition, physical state, and can impact life on Earth's surface. Now, we also know that movement in the mantle, which is caused by variations in heat from the core, causes the plates to shift, which further can cause earthquakes and volcanic eruptions. Therefore, these earthquakes and volcanic eruptions affect the lives and environment on earth.
Also, here a hot spot is said to be an area on Earth over a mantle plume. Hot spot can also be understood as an area under the rocky outer layer of Earth, called the crust, where magma is hotter than surrounding magma. This magma plume causes melting and thinning of the rocky crust and it also widespread volcanic activity.
Since, there are many advantages and limitations of utilizing energy obtained from the hot spots. The one major advantage of utilizing energy from this hotspot is that the cost of production of electricity is very less compared to other sources of electricity.
Further, one major limitation of utilizing energy from this hotspot is that there are very few commercial sites that use this energy, this source of energy is used only in limited applications.

Note:
Here, we should remember that, a light-year is that distance, which light travels in one Earth year. This term is used to express astronomical distance. One light-year is about 6 trillion miles. Also, one should note that there are different numbers of days in a year of different planets. If we take an example of Mars, as Mars is little slower than Earth and also, farther from the Sun, there are 687 days in a Mars year.