A planet has a mass of about 0.1075 times the mass of Earth and bout 0.533 times

Question

A planet has a mass of about 0.1075 times the mass of Earth and bout 0.533 times the diameter of Earth. The acceleration of a body tai g the surface of the planet is about: 0.30 m/s2 1.4 m /s^2 2.0 m/s^2 3.7 m/s^2 26 m/s^2 The escape velocity at the surface of Earth is approximately 11 km/s. What is the mass, in units of Mn (the mass of the Earth), of a planet with twice the radius of Earth for which the escape speed is twice that for Earth: 2 ME 4 ME 8 ME 1/2ME 1/4ME A planet orbiting a star in a galaxy far, far away has mass of 8.9 times 10^22 kg and radius of 1822 km. What is the escape velocity from the surface of the planet? 1.2 km/s 1.4 km/s 1.8 km/s 2.2 km/s 2.6 km/s

Explanation / Answer

The general gravitational attraction formula is
F = GMm/r²
from which g= F/m = GM/r²
To find the value of acceleration on Venus relative to the value on earth, we have
g*0.1075/(0.533)²
=0.378*g
= 3.7

Escape Velocity = (2*G*M/r)^1/2 = 11
FOr the planet =>
x/2(11)^2 = 22^2
x/2 = 4
x = 8 times mass of earth

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