Answer:
[tex]1.156\times 10^{24}\ kg[/tex]
Explanation:
Given:
Gravity of Mars = 0.38 times the gravity at Earth
Gravity of Earth is, [tex]g_{Earth}=9.8\ m/s^2[/tex]
Radius of Mars (R) = 3400 km
Mass of mars (M) = ?
We know that, the acceleration due to gravity of a planet of mass 'M' and radius 'R' is given as:
[tex]g=\dfrac{GM}{R^2}[/tex]
Now, as per question:
[tex]g_{Mars}=0.68g_{Earth}[/tex]
Plug in 9.8 for [tex]g_{Earth}[/tex] and solve for [tex]g_{Mars}[/tex]. This gives,
[tex]g_{Mars}=0.68\times 9.8=6.67\ m/s^2[/tex]
Now, plug in this value in the above equation and solve for 'M'. This gives,
[tex]6.67=\frac{6.67\times 10^{-11}M}{(3400\times 10^3)^2}\\\\1.156\times 10^{13}=10^{-11}M\\\\M=\frac{1.156\times 10^{13}}{10^{-11}}\\\\M=1.156\times 10^{24}\ kg[/tex]
Therefore, the mass of Mars is [tex]1.156\times 10^{24}\ kg[/tex].
