# The Rocket Equation

by adphysics
Tags: equation, rocket
 P: 7 In deriving the rocket equation, there is one part I don't understand. The velocity of exhaust with respect to the body is assumed to be constant, where: v(exhaust wrt body)=v(exhaust wrt inertial)-v(body wrt inertial) So assuming a constant mass flow rate, the rocket propellant exerts a constant force on the rocket and hence in space, uniform acceleration. But how can an observer on the accelerating rocket observe the rocket propellant being ejected with a constant velocity?
HW Helper
P: 2,328
 Quote by adphysics ... the rocket propellant exerts a constant force on the rocket and hence in space, uniform acceleration.
This is not correct. The mass of the rocket decreases at a rate equal to the exhaust mass rate. The constant exhaust velocity should be w.r.t the rocket.
 P: 7 Oops. So assuming a constant mass flow rate the propellant exerts a constant force on the rocket so the rocket's acceleration increases as follows: a(t)=F[1/m(t)] where F is a constant (until fuel runs out) where m(t) is the mass of the rocket at time t. m(t)=m(initial)-bt where b is a constant (mass flow rate) Hence v_rocket(t)=-Fln(m(t))/b assuming v(0)=0 But why would an observer in the rocket observe a constant propellant velocity?
HW Helper
P: 2,328

## The Rocket Equation

 Quote by adphysics ... why would an observer in the rocket observe a constant propellant velocity?
Because the propelling mechanism is in the rocket.
 P: 7 Oh, yeah. The engine is on the back of the rocket, so it accelerates with the rocket, so if an engine ejects exhaust at a velocity v, then this is what is observed from the rocket's point of view. Now I feel somewhat embarrassed, but at least the rocket equation makes sense now.
HW Helper
P: 2,328
 Quote by adphysics Now I feel somewhat embarrassed, ...
You should not. No one knows everything. You should only feel embarrassed if you refuse to ask a question out of fear of sounding stupid. Don't let your transient embarrasment prevent your permanent understanding:
 Quote by adphysics ... the rocket equation makes sense now.
Have fun learning.

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