# Homework Help: Planetesimal Accretion

1. Jun 3, 2014

### spinnaker

Kinda stumped. The question gives three equations and I don't know what to do with them, because given the equations there's always more than one unknown. Any assistance/tips would be appreciated!

If a planetesimal has a cross-sectional area of πR2 (where R is the planetesimal's radius) and is sweeping through a cloud of smaller particles of fixed size with a velocity V, the number of collisions per second will be:

dn/dt = (πR2N)/m

where ρN=the space density (kg/m3) of particles in the cloud and m=the mass of each particle.

If each collision results in the target particles sticking to the planetesimal, the planetesimal will gain mass at a rate of

dM/dt = πR2N

where M=the planetesimal mass.

The time to grow to radius R is

t = (4R/V)/(ρPN)

where ρP=the density of the planetesimal itself. (Assume that ρN and V stay constant as particles are swept up.)

Assuming that a reasonable value for the density of accretable material in inner part of the early solar nebula is ρN = 10-7 kg/m3, estimate the time to accrete a body of 1,000 km radius. Assume a reasonable ρP.

2. Jun 4, 2014

### Simon Bridge

You are given an equation t=... and you know all the variables.

3. Jun 4, 2014

### ehild

That was a duplicate post. Solved in the other thread in Introductory Physics.

ehild