Rocket thrust is rocket mass times acceleration

Assuming we are at rest relative to an inertial reference frame, we observe a rocket through space with no gravitational or atmospheric drag forces acting on it. The mass of the rocket changes as it burns fuel and releases the products of burning, the total mass of the system does not change.

Conditions:

1. The fuel consumption rate is constant.

2. The velocities are non-relativistic.

Notes:

1. The quantity \(R v_\text{rel}\) is called the thrust of rocket engine.

2. The rate \(R\) of fuel consumption is defined as

   \[R = - \frac{d m}{d t}\]

   where \(m\) is the rocket mass.

Links:

1. Equation 9-87 on p. 242 of “Fundamentals of Physics” by David Halladay et al., 10th Ed.

fuel_consumption_rate

The rate of fuel consumption, or mass_flow_rate of exhaust. See Note for the definition.

Symbol:

R

Latex:

\(R\)

Dimension:

mass/time

relative_speed

The speed of the rocket relative to its products.

Symbol:

v_rel

Latex:

\(v_\text{rel}\)

Dimension:

velocity

acceleration

The acceleration of the rocket.

Symbol:

a

Latex:

\(a\)

Dimension:

acceleration

mass

The mass of the rocket

Symbol:

m

Latex:

\(m\)

Dimension:

mass

law

R * v_rel = m * a

Latex:

\[R v_\text{rel} = m a\]