Question

the mass of an exoplanet is 9 times the mass of the earth and its radius is 4 times the radius of the earth. a) if the mass of a person on the surface of the earth is 80 kg what will be his mass and weight on the surface of the exoplanet? b) if the person can jump to a height of 2 m on the surface of the earth how high can he jump on the exoplanet? c) compare the gravitational potential on the surface of planet a to that of planet b.

Answer 1

a)

$$m_P=m_E=m=80\ kg\\W_P=\frac{GM_Pm}{R^2_P}=\frac{9GM_Em}{4^2R^2_E}=0.5625W_E\\=0.5625(80)(9.8)=441\ N$$

b)

$$v^2=const=2g_Eh_E=2g_Ph_P\\gh_E=0.5625gh_P\\2=0.5625h_P\\h_P=3.56\ m$$

c)

$$V_P=\frac{GM_P}{R_P}=\frac{9GM_E}{4R_E}=2.25V_E$$