The mass of Earth is 9.31 times the mass of Mars,and the radius of Earth is 1.88 times the radius of Mars.The escape speed for Mars is what percent of the escape speed for Earth?

Question

Quizplus · Accepted Answer

The escape speed is given by:

v = sqrt((2GM)/r)

Where v is escape speed, G is gravitational constant, M is mass of the planet, and r is the radius of the planet.

Let's first find the ratio of the mass of Earth to Mars:

M_E / M_M = 9.31

Let's now find the ratio of the radius of Earth to Mars:

r_E / r_M = 1.88

Now let's use these ratios to write the escape speeds in terms of one another:

v_M / v_E = sqrt((2G(M_M / r_M))/(2G(M_E / r_E)))

v_M / v_E = sqrt((M_M / r_M)/(M_E / r_E))

v_M / v_E = sqrt((M_M / M_E)*(r_E / r_M))

Now we can substitute in the given ratios:

v_M / v_E = sqrt((1/9.31)*(1.88))

v_M / v_E = sqrt(0.202)

v_M / v_E = 0.449

Finally, we convert to a percentage:

v_M = v_E * 0.449 = 44.9% v_E

Therefore, the answer is C.

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