Question

The radius of Jupiter is 11 times the radius of the Earth. Calculate the ratio of volumes of Jupiter and the Earth. How many earths can Jupiter accommodate?

Answer 1

Hint: Jupiter is composed primarily of hydrogen and helium. It weighs in at 1.9 x1027 kilograms. Although it is significantly more massive than Earth, it is only a fifth as dense, at 1,326 kg/m3, because it is made of gas rather than rock.

Complete Step-by-step Solution
Consider two spheres one is Earth, and another one is Jupiter with radii Rand R’. In the given question, we have that the radius of Jupiter is 11 times the radius of the Earth.
Thus, R’=11 R
The volume of a sphere is $ = \dfrac{4}{3}\pi {r^3}$
Volume of Earth $ = \dfrac{4}{3}\pi {R^3}$
And the volume of Jupiter $\dfrac{4}{3}\pi{{R^{‘}}^3}$
=$\dfrac{4}{3}\pi {(11R^3)}$
=$(1331)\dfrac{4}{3}\pi {R^3}$
Thus the ratio of the volume of Jupiter and Earth $ = \dfrac{{1331\left( {\dfrac{4}{3}\pi {R^3}} \right)}}{{\dfrac{4}{3}\pi {R^3}}} = 1331$

Hence, the ratio suggests that Jupiter can accommodate 1331 several piles of Earth in it.

Additional information:
Jupiter is so massive that all the other planets in the solar system could merge inside it. More than 3 Earths would fit inside Jupiter. Jupiter has a diameter of about 88,695 miles, which is more than 11 times the diameter of Earth. Its volume is over 1,300 times the volume of Earth. That means that Jupiter is so massive that over 1,300 Earths could fit inside of it.

Note:
Jupiter is the fifth planet from the Sun and the largest in the Solar System. It is a Jovian planet with a mass one-thousandth that of the Sun, but two-and-a-half times that of all the other planets within the Solar System combined.