Physics of Rocketry: Distance Traveled

by roldy
Tags: distance, physics, rocketry, traveled
roldy is offline
May1-11, 11:51 PM
P: 194
Calculate the firing times for the acceleration and deceleration leg of the mission described below and also the distance traveled for each leg. I also need to calculate the initial mass of the vehicle.

1) acceleration leg from zero velocity to a final velocity of 25,000 m/s.
2) 360 'cruise' non-acceleration leg (constant velocity) at 25,000 m/s; systems shut down.
3) deceleration leg (delta V=25,000 m/s)

This question is part of a bigger question of which I had to solve a couple things for. What's given:

ISP=4000 seconds
g=9.81 m/s^2
[tex]m_L[/tex]=7000 kg

I have calculated the mass flow rate of the propellant to be .006371 kg/s and the mass of the engine to be 3.42485 kg. Here is my work thus far.

initial mass=mass of engine + mass of payload + mass of propellant

[tex]\frac{m_0-m_p}{m_0}=e^{\frac{-\Delta V}{ISPg_0}}}[/tex]

So I solve the above equation for [tex]m_p[/tex] and put into the first equation to obtain the equation below solved for [tex]m_0[/tex].


So plugging in the numbers where [tex]\Delta V[/tex]=25000, I get the initial mass of the vehicle to be 13243.5 kg. This seems reasonable.

Now this is where I get confused, how do I go about solving for the propellant mass in each leg and the distance traveled. I believe that I have to do some sort of integration for the distance traveled due to the mass constantly decreasing. Is there an equation or integration set up for this already?
Phys.Org News Partner Science news on
SensaBubble: It's a bubble, but not as we know it (w/ video)
The hemihelix: Scientists discover a new shape using rubber bands (w/ video)
Microbes provide insights into evolution of human language

Register to reply

Related Discussions
Physics problem involving a gravitational change based on distance traveled. Introductory Physics Homework 25
Distance traveled! Introductory Physics Homework 11
Distance Traveled Introductory Physics Homework 5
Distance traveled, v->c Advanced Physics Homework 13
distance traveled Introductory Physics Homework 1