Chapter 5: Q35. (page 134)

Given that the acceleration of gravity at the surface of Mars is 0.38 of what it is on Earth, and that Mars’ radius is 3400 km, determine the mass of Mars.

Expert verified

The mass of Mars is $6.5 \times 10^{23} kg$ .

Step by step solution

The acceleration due to gravity of Mars is $g_{m} = 0.38 g$ .

The radius of Mars is $r_{m} = 3400 km$ .

In order to estimate the mass of the planet Mars, the formula of acceleration due to gravity will be used along with the radius of the Mars.

The relation of gravitational acceleration is given by,

$\begin{matrix} g_{m} = 0.38 g \\ \frac{G m_{m}}{{r_{m}}^{2}} = 0.38 \frac{G m}{r^{2}} \\ m_{m} = 0.38 {r_{m}}^{2} \frac{m}{r^{2}} \end{matrix}$

Here, g is the Earth’s gravitational acceleration, $m_{m}$ is the mass of Mars, r is the radius of the Earth and m is the mass of the Earth.

On plugging the values in the above relation.

$\begin{array}{l} m_{m} = 0.38 {(3400 km)}^{2} (\frac{(5.98 \times 10^{24} kg)}{{(6380 km)}^{2}}) \\ m_{m} = 6.5 \times 10^{23} kg \end{array}$

Thus, $m_{m} = 6.5 \times 10^{23} kg$ is the required mass.

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