A team of astronauts is on a mission to land on and explore a large asteroid. In

Question

A team of astronauts is on a mission to land on and explore a large asteroid. In addition to collecting samples and performing experiments, one of their tasks is to demonstrate the concept of the escape speed by throwing rocks straight up at various initial speeds. With what minimum initial speed Vesc will the rocks need to be thrown in order for them never to fall back to the asteroid? Assume that the asteroid is approximately spherical, with an average density p = 2.41 x 10^8 g/m^3 and volume V = 1.94 x 10^12 m^3. Recall that the universal gravitational constant is G = 6.67 x 10^-11 N.m^2/kg^2. vesc= m/s

Explanation / Answer

Given that,

density = 2.41 x 108 g/m3 = 2.41 x 105 kg/m3

Volume = 1.94 x 1012 m3

G = 6.67 x 10-11

We know that, mass = density x volume =  2.41 x 105 x  1.94 x 1012 = 4.57 x 1017 kg

4/3 pi r3 = 1.94 x 1012 m3 which gives us r = 7800 m

Escape velocity is given by

v = sqrt(2Gm)/r = sqrt (2x6.67 x 10-11 x 4.57 x 1017 )/ 7800

v = 88.47 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.