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As planets with a wide variety of properties are being discovered

outside our solar system, astrobiologists are considering whether and how life

could evolve on planets that might be very different from earth. One recently

discovered extrasolar planet, or exoplanet, orbits a star whose mass is 0.70

times the mass of our sun. This planet has been found to have 2.3 times the

earth’s diameter and 7.9 times the earth’s mass. For planets in this size range,

computer models indicate a relationship between the planet’s density and

composition:

Based on these data, what is the most likely composition of this planet? (a)

Mostly iron; (b) iron and rock; (c) iron and rock with some lighter elements; (d)

hydrogen and helium gases.

Step by step solution

01

Identification of given data

The mass of the planet is,$m=7.9m_E$.

The radius of planet is, $R=2.3R_E$.

02

Concept of density

The density of a material is equal to the product of its mass and

volume.Density of material is determined by the mass, size, and arrangement

of its atoms.

The density is given by,

$\mathrm{ÒÏ}=\frac{m}{V}$… (i)

03

Determination of density of the planet

The density of planet can be evaluated using equation (i),

$$\begin{gathered} \mathrm{ÒÏ}=\frac{m}{{\displaystyle \frac{4}{3}}{\mathrm{Ï€¸é}}^3} \\ \mathrm{ÒÏ}=\frac{7.9m_E}{{\displaystyle \frac{4}{9}}\mathrm{Ï€}{\left(2.3{\mathrm{R}}_{\mathrm{E}}\right)}^3} \\ \mathrm{ÒÏ}=\frac{7.9}{{\left(2.3\right)}^3}\frac{m_E}{{\displaystyle \frac{4}{3}}\mathrm{Ï€}{\left({\mathrm{R}}_{\mathrm{E}}\right)}^3} \\ \mathrm{ÒÏ}=0.65{\mathrm{ÒÏ}}_E \end{gathered}$$

Thus, the most likely composition of the planet is iron and rock with some lighter

elements. Option c is correct.

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