Question

The mean diameters of Mars and Earth are 6.9 x 10^3 km and 1.3 x 10^4 km, respectively. The mass of Mars is 0.11 times Earth’s mass.

a) What is the ratio of the mean density (mass per unit volume) of Mars to that of Earth?
b) What is the value of the gravitational acceleration on Mars?
c) What is the escape speed on Mars?

Answer 1

Answer:

Explanation:

a ) density = mass / volume

density of mars / density of earth

= (mass of mars/mass of earth) x (volume of earth / volume of mars)

= (mass of mars/mass of earth) x (diameters of earth / diameters of mars)³

=   0.11 x (130/69)³

= .73

b )

gravitational acceleration (g) = GM/R²

Gravitational acceleration on mars / Gravitational acceleration on earth

= (mass of mars / mass of earth) x (radius of earth / radius of mars )²

= .11 x (130/69 )²

= .39

Gravitational acceleration on mars = .39 x Gravitational acceleration on earth

Gravitational acceleration on mars =  9.8 x .39

= 3.82 m/s

c ) Escape velocity $\sqrt{2gR }$

c ) escape speed of mars / escape velocity of earth

= [( g on mars / g on earth ) x ( radius of mars / radius of earth )]°⁵

= √(.39 x 69/130)

= .4549

escape speed of mars = .4549  x escape velocity of earth

= .4549  x 11.2km/s

= 5.1 km / s