Gravitation (Potential Energy)

[Oijl]

1. The problem statement, all variables and given/known data
How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?

The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2


2. Relevant equations



3. The attempt at a solution
I would have thought I could just see how much energy a particle of mass m has moving at 1000 m/s, and then see what radius r would be necessary to produce the gravitation potential energy of the asteroid-particle system equal to the initial kinetic energy. When I do this, solving for r gives me a very small number.

[Hootenanny]

1. The problem statement, all variables and given/known data
How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?

The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2


2. Relevant equations



3. The attempt at a solution
I would have thought I could just see how much energy a particle of mass m has moving at 1000 m/s, and then see what radius r would be necessary to produce the gravitation potential energy of the asteroid-particle system equal to the initial kinetic energy. When I do this, solving for r gives me a very small number.
Note that the gravitation field is only valid near the surface of the asteroid. When you move away from the surface you need to use the full gravitational potential formula,

U = \frac{GM}{r}

[Oijl]

I know; isn't gravitational potential energy described by

U = -(GMm)/r ?

So can't I say that plus (1/2)mv^2 equals zero, and solve for r? When I do that, I get 1158815 meters, but that's not the right answer.

[Dweirdo]

Hi,
"The radius of the asteroid is 565000 m, and the gravitational acceleration near the surface is 2.7 m/s^2"
With this information You can find the mass of the asteroid.
F=mg , F=GMm/R^2 --> g=GM/R^2 while g=2.7,R=565000.and G=6.67*10^-11 You can find M.

now, the initial energy of the body is the kinetic energy+potential energy, when the potential energy as stated in the post above is U=-GMm/R.
What happens in the highest point?
The body's kinetic energy=0 and he has potential energy equal to -GMm/R+h(max).
by the energy conservation------> Ei=Ef while i=initial and f=final.
note:the little m, aka the mass of particle goes away.
note 2:sometimes i wrote body instead of particle.
Good luck! Tell me if You get the wrong answer
note 3: I've seen Your message and You wrote that Ke+Up=0,seems logical, but I don't think its right...well what is the right answer?

[Hootenanny]

I know; isn't gravitational potential energy described by

U = -(GMm)/r ?

So can't I say that plus (1/2)mv^2 equals zero, and solve for r? When I do that, I get 1158815 meters, but that's not the right answer.
The question asks for the distance from the surface, whereas r is the distance from the centre of the asteroid.