91影视

The given data and data from Appendix F can be listed below as,

• The mass of the planet is,$M_P=5.5M_E=(5.5)(5.97脳{10}^{24}kg)=3.28脳{10}^{25}kg$. Where$M_E$is earth鈥檚 mass.
• The density of the planet is,${蚁}_P=1.76鈥�g/c{m}^3$.
• The radius of the earth is, $r_E=6.37脳{10}^6鈥�m$.

The volume of an object is the amount of three-dimensional space it takes up, whereas density is the mass of the unit volume of the object.

The volume of the planet is given by,

$V_P=\frac{M_P}{p_P}$

Here, $鈥�M_P$is the planet鈥檚 mass and $p_p$is the planet鈥檚 density.

Substitute the values in the formula of $V_P$, and we get,

$$\begin{gathered} V_P=\frac{3.28脳{10}^{25}\mathrm{kg}}{1.76\mathrm{g}/{\mathrm{cm}}^3}\left(\frac{1\mathrm{g}/{\mathrm{cm}}^3}{1000\mathrm{kg}/{\mathrm{m}}^3}\right) \\ =1.86脳{10}^{22}{\mathrm{m}}^3 \end{gathered}$$

Consider the planet as a sphere. Its volume can be expressed as,

$V_P=\frac{4\mathrm{蟺}}{3}{r}_P^3$

Here,$r_P$ is the planet鈥檚 radius.

Solution of the above equation for$r_P$ gives,

$r_p={\left(\frac{3V_P}{4\mathrm{蟺}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$

Substitute all the values in the above,

$$\begin{gathered} r_P={\left(\frac{3脳\left(1.86脳{10}^{22}{\mathrm{m}}^3\right)}{4蟺}\right)}^{1/3} \\ =1.64脳{10}^7\mathrm{m}\left(\frac{1\mathrm{km}}{1000\mathrm{m}}\right) \\ =1.64脳{10}^4\mathrm{km} \end{gathered}$$

Thus, the planet鈥檚 radius is $=1.64脳{10}^4\mathrm{km}$.

The planet鈥檚 radius is given by,

$r_P=1.64脳{10}^4鈥�km$

The radius oftheplanet in terms of earth鈥檚 radius can be expressed as,

$r_p=\left(\frac{r_p脳r_E}{r_E}\right)$

Here, $r_E$is the radius of the earth whose value is $r_E=6.37脳{10}^6鈥�m$.

Substitute values in the above equation, and we get,

$$\begin{gathered} r_P=\left(\frac{1.64脳{10}^7\mathrm{m}脳r_E}{6.37脳{10}^6\mathrm{m}}\right) \\ =2.57r_E \end{gathered}$$

Thus, the planet鈥檚 radius in terms of the earth鈥檚 radius $\left(r_E\right)$is $2.57r_E$.