Venus has a mass of about 0.0558 times the mass of Earth and a diameter of about 0.381 times the diameter of Earth. The acceleration of a body falling near the surface of Venus is about:

Question

Venus has a mass of about 0.0558 times the mass of Earth and a diameter of about 0.381 times the diameter of Earth. The acceleration of a body falling near the surface of Venus is about: (a) 0.21 m/s2 (b) 1.4 m/s2 (c) 2.8 m/s2 (d) 3.97 m/s2 (e) 25 m/s2

Answer 1

Hi Ina,

For this question we would use newton's formula for gravitation:

Fg = GmM/r^2

Where G is the gravitational constant, m is the mass of the falling object, M is the mass of the planet, and r is the distance from the center of the planet. Implementing the formula F=ma we can reduce this down to:

ma = GmM/r²

a=GM/r²

Using g = 9.81 m/s² to represent the gravitational acceleration of Earth, we can substitute in the size and mass of Venus to get the gravitational acceleration of Venus relative to Earth:

g=GM_Earth/r_Earth²

a_Venus = GM_venus/r_Venus² = G(0.0558 M_Earth)/(0.381 r_Earth)² = 0.0558/(0.381)² * GM_Earth/r_Earth²

a_Venus = 0.0558/(0.381)² * g = 0.3844 *9.81m/s² = 3.8 m/s²