I am using the derivative of momentum (dp/dt) with Newton’s 3rd Law with the gravitational force of Earth.
F - [Force of gravity on rocket] = dp/dt
F - (G * m_e * m_r / r2 ) = v * dm/dt + ma
F = Force created by fuel (at time t)
G = Gravitational Constant
m_e = Mass of Earth
m_r = Mass of...
I want to try to derive the rocket equation and then add additional effects like gravity, air resistance, etc. Here's the equation that I found online:
p (momentum) = mass * velocity
F (force) = Δp / Δt
The Attempt at a Solution
pi = mv
The problem states:
Typical chemical fuels yield exhaust speeds of the order of 103 m/s. Let us imagine we had a fuel that gives v0 = 3 × 105 m/s. What initial mass of fuel would the rocket need in order to attain a final velocity of 0.1c for a final mass of 1 ton?
I derived the equation in the...
A rocket with initial mass of m0. The engine that can burn gas at a rate defined by m(t)=m0-αt, and expel gas at speed (relative to the rocket) of u(t)=u0-βt. Here, m0, α, u0, and β are all constants. Assume the lift-off from ground is immediate
a) The rocket speed v(t)=...