Answer to Question #157893 in Physics for Jm

Question

You’re involved in the design of a mission carrying humans to the surface of the 

planet Mars, which has a radius 3.37x106m and a mass of 6.42x1023 kg. The 

earth weight of the Mar’s lander is 39,200 N. Calculate its weight and the 

acceleration due to Mar’s gravity at 6.0 x 106 m above the surface of Mars.

Answer 1

$$g_M=\dfrac{GM_M}{(R_{M}+h)^2},$$ $$g_M=\dfrac{6.7\cdot10^{-11}\ \dfrac{Nm^2}{kg^2}\cdot 6.42\cdot10^{23}\ kg}{(3.37\cdot10^6\ m+6\cdot10^6\ m)^2}=0.49\ \dfrac{m}{s^2}.$$

The mass of the Mar’s lander:

$$m=\dfrac{W}{g}=\dfrac{39200\ N}{9.8\ \dfrac{m}{s^2}}=4000\ kg.$$

The weight of the Mar’s lander at a height $h=6\cdot10^6\ m$ above the surface of Mars will be:

$$W=mg_M=4000\ kg\cdot0.49\ \dfrac{m}{s^2}= 1960\ N.$$