Asteroid 433 Eros is one of the largest near-Earth asteroids. For purposes of this problem, assume it is spherical. The value of g at its surface is 0.00600 m/s² and the escape velocity is only 9.95 m/s. What is the radius of Eros? A) 8250 m B) 16,000 m C) 1600 m D) 800 m E) 400 m

Question

Quizplus · Accepted Answer

Using the formula for escape velocity $ v_e = \sqrt{2gr} $, where $ g = 0.00600 \, \text{m/s}^2 $ and $ v_e = 9.95 \, \text{m/s} $, we can solve for the radius $ r $. Rearranging gives $ r = \frac{v_e^2}{2g} $. Substituting the given values, $ r = \frac{(9.95)^2}{2 \times 0.00600} \approx 8250 \, \text{m} $.

Asteroid 433 Eros Is One of the Largest Near-Earth Asteroids