Chapter - 7 Stars and the Solar System

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Q
Stars and the Solar System

Question:

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

Answer:

Given:

The radius of Jupiter is 11 times the radius of the Earth.

R_J=11R_E

Jupiter and Earth are spherical in shape, therefore the volume of planets will be

 frac{4}{3}pi{r}^3

Volume of earth = frac{4}{3}pi{(R_E)}^3

Volume of Jupiter = frac{4}{3}pi{(R_J)}^3

Using the given relation R_J=11R_E

Volume of Jupiter = frac{4}{3}pi{(11R_E)}^3

The ratio of volumes of Jupiter and Earth will be:

frac{Volume of Jupiter}{Volume of Earth}= frac{frac{4}{3}pi{(11R_E)}^3}{frac{4}{3}pi{(R_E)}^3}

frac{Volume of Jupiter}{Volume of Earth}= frac{1331frac{4}{3}pi{(R_E)}^3}{frac{4}{3}pi{(R_E)}^3}

frac{Volume of Jupiter}{Volume of Earth}= 1331

This ratio of volumes of Jupiter and Earth indicates, that Jupiter can accommodate 1331 Earth.


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