Planets are big.

An asteroid has a radius of 580 km and a gravitational acceleration at the surface of 4.0 m/s2.

How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1000 m/s?  (It never escapes orbit)

ITT nonsense being passed off as a legitimate question.

well..if it starts on the surface with a radial speed of 1000 m/s it won't leave the ground.

radial speed meaning tangential to the surface of the asteroid?

>>4
Maybe it means speed along some axis radiating from the center of the asteroid.

But that doesn't make much sense either, since the asteroid is likely not very close to spherical.

omg Energie=GmM/r=(1/2) m*v^2 Solve for r. And please, ask newb questions like this anywhere but here... This is for REAL science (also you don't need acceleration of gravity)

>>6

unless I'm missing something entirely... the mass of the asteroid M isn't specified
you're going to need to calculate the energy required to lift the particle from the surface, r (radius of the asteroid) to some final distance, Rf (final radius)...

the energy required is = int(g*m*(r/s)^2)ds from Ra to Rf...
s = distance from the center of the object
everything is constant except s, so this equals:

mgr^2[-Rf^(-1) - r^-1 ] = mgr - m*g*r^2/Rf

take this equal to the object's intial kinetic energy, 1/2*m*v^2

i.e. 1/2*m*v^2 = m*g*r - m*g*r^2/Rf, the mass cancels out leaving

1/2v^2 = g*r - g*r^2/Rf

solving for Rf, Rf = g*r^2/(g*r-1/2*v^2)

which makes since, because if the intial velocity is zero, Rf is just r, the radius of the asteroid (you didnt go anywhere)

plugging in g=4m/s^2, r=580*10^3m, v = 1000m/s


Rf = 740*10^3m (740 km) (2 sig figs).

anyone else verify this?

>>7

oh yea, on the intial integral it should say just r instead of "Ra
" i changed this mid way through and forgot about it.

>>5
Radial speed does make sense. Take the center of mass of the asteroid and lets its position vector be denoted c, take the position vector p of the object, then the vector p-c. This is the radial vector. Just take the component of velocity vector v along p-c, which is equal to (p-c)*v ((p-c)/||p-c||^2) where * denotes the dot product. Remember, if something does not have a geometric center, assume that the "center" is the center of mass.