Given that the acceleration of gravity at the surface of Mars is0.38 of what it is one Earth, and that Mars’ radius is 3400 km,determine the mass of Mars.

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,

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].