Question

For a mission characterized by a velocity increment v and a

rocket of constant thrust level T, derive an expression for the
optimum specific impulse in terms of power supply specific mass and
the initial total mass of the spacecraft.

Answer 1

To derive an expression for the optimum specific impulse, we need to consider the thrust and velocity increment of the rocket. The specific impulse is defined as the thrust divided by the rate of mass flow.

Step-by-step explanation:

To derive an expression for the optimum specific impulse, we need to consider the thrust and velocity increment of the rocket. The thrust is equal to the rate of change of momentum of the fuel, which can be calculated using the rate at which mass is being ejected and the velocity of the ejected fuel. The specific impulse is defined as the thrust divided by the rate of mass flow. By substituting the expressions for thrust and rate of mass flow, we can derive an expression for the optimum specific impulse in terms of the power supply specific mass and the initial total mass of the spacecraft.

Specific impulse = (T / (dm/dt))