# Question about mass growth rate for individual planetesimals

In one stage of classic accretion, the mass growth rate with time (dm/dt) for individual planetesimals is proportional to $$m^{2/3}$$ and in another stage it is proportional to $$m^{4/3}$$. My question is why are the exponents different? Which stage is a runaway and which stage comes first?

• There are different theories of planetesimal formation - can you clarify where you are finding these relations, and more about what that source says about what the different stages are? – Eric Jensen Jun 12 '20 at 17:51
• Some superficial knowledge of differentiation is sufficient to conclude that solutions blow up in finite time for m in the 4/3 power and grow indefinitely as time cubed for m in the 2/3 power. – Incnis Mrsi Dec 22 '20 at 18:50