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 istimes the mass of our sun. This planet has been found to havetimes the earth’s diameter andtimes the earth’s mass. For planets in this size range, computer models indicate a relationship between the planet’s density and composition:

How many times the acceleration due to gravity gnear the earth’s surface is the acceleration due to gravity near the surface of this exoplanet? (a) About 0.29 g ; (b) about 0.65 g; (c) about 1.5 g; (d) about 7.9 g.

The given data can be listed below as-

• The acceleration due to the gravity near the surface of the earth is, $g_E$.
• The acceleration due to gravity near the surface of the exoplanet is, g .

The gravitational acceleration is referred to as an object that receives an acceleration because of the gravitational force acting on that object.

The gravitation acceleration is given by,

$g=\frac{GM}{R^2}........\left(1\right)$

Here, g is the acceleration due to gravity near the surface of the exoplanet, Gis the gravitational constant, Mis the mass of the planet and R is the radius of the planet.

Here, it is given that the mass of the exoplanet is 7.9 times that of the Earth and the radius of the exoplanet is 2.3 times the radius of the Earth.

Substituting the values in the equation i), the acceleration due to gravity can be evaluated using equation (i),

$$\begin{gathered} \mathrm{g}=\frac{\mathrm{G}(7.9{\mathrm{m}}_{\mathrm{E}})}{{(2.3{\mathrm{R}}_{\mathrm{E}})}^2} \\ \mathrm{g}=\frac{7.9}{{(2.3)}^2}\frac{{\mathrm{Gm}}_{\mathrm{E}}}{{\mathrm{R}}_{\mathrm{E}}^2} \\ \mathrm{g}=1.5{\mathrm{g}}_{\mathrm{E}} \end{gathered}$$

Although the mass of this planet is 7.9 times that of the Earth, g at its surface is only $1.5g_E$because the planet has 2.3 times the radius of the Earth, which puts the surface further out from its core than it is in the case with the Earth.

Thus, the acceleration due to gravity is about 1.5g near the earth’s surface.