You stand on a spherical asteroid of uniform density whose mass is 2.51016 kg an

Question

You stand on a spherical asteroid of uniform density whose mass is 2.51016 kg and whose radius is 11 km (11103 m). These are typical values for small asteroids, although some asteroids have been found to have much lower average density and are thought to be loose agglomerations of shattered rocks. You want to figure out how fast you have to throw the rock so that it never comes back to the asteroid and ends up traveling at a speed of 4 m/s when it is very far away.

The question is how fast do you have to throw the rock so that it never comes back to the asteroid and ends up traveling at a speed of 4 m/s when it is very far away? (Note the launch speed is relative to you.

Explanation / Answer

The radius of the asteroid is R = 11000 m

Mass of the asteroid is M = 2.5*1016 kg

The velocity of the object at farthest distnace is vf = 4 m/s

At the farthest point, the gravitational potential is zero.

Let v be the projected speed of the object on the asteroid

The gravitational potential at the surface is U = -GM/R

Let m be the mass of the stone, then

The potential energy of the stone is Ui = -GMm/R

The potential energy at the farthest point is Uf = 0

The kinetic energy of the stone at surface is Ki = 0.5mv2

The kinetic energy of the stone at farthest point is Kf = 0.5mvf2

Therefore according to the conservation of energy

-GMm/R = 0.5mvf2 - 0.5mv2

-(6.67*10-11 Nm2/kg2)(2.5*1016 kg)/(11000 m) = 0.5(4 m/s)2 - 0.5(v2)

v = 17.865 m/s

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

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