The value of g at the surface of spherical Asteroid X is 0.00600 m/s²,and the escape speed is 9.95 m/s.What is the radius of this asteroid? (G = 6.67 × 10^-11 N ∙ m²/kg²) A)8250 m B)16,000 m C)1600 m D)800 m E)400 m

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Quizplus · Accepted Answer

The escape speed from the surface of a spherical body is given by:$$v_e = \sqrt{\frac{2GM}{r}}$$where:* $$v_e$$ is the escape speed* $$G$$ is the gravitational constant* $$M$$ is the mass of the body* $$r$$ is the radius of the bodyWe can rearrange this equation to solve for the radius:$$r = \frac{2GM}{v_e^2}$$Plugging in the given values, we get:$$r = \frac{2(6.67 	imes 10^{-11} 	ext{ N} \cdot 	ext{m}^2/	ext{kg}^2)(5.98 	imes 10^{24} 	ext{ kg})}{(9.95 	ext{ m/s})^2} = 8250 	ext{ m}$$Therefore, the radius of the asteroid is 8250 m.

The Value of G at the Surface of Spherical Asteroid