Assume you have a rocket that requires a change in velocity of ¦¤V¡Ö9.6km/s . There are two options for the propulsion system --- 1. chemical and 2. electric --- each with a different specific impulse.

Question

Assume you have a rocket that requires a change in velocity of ¦¤V¡Ö9.6km/s . There are two options for the propulsion system --- 1. chemical and 2. electric --- each with a different specific impulse.

Using the setting of g 0 =9.81m/s^2 to calculate the propellant fraction required to achieve the necessary ¦¤V for each of propulsion system answer the following two questons.

Question 1

First, consider a cryogenic chemical propulsion system with Isp ¡Ö450s . Enter the required propellant fraction as a proportion with at least 2 decimal places

Question 2

Next, consider an electric propulsion system with Isp ¡Ö2000s . Enter the required propellant fraction as a proportion with at least 2 decimal places

Answer 1

To calculate the propellant fraction required for each propulsion system, we need to use the rocket equation:

¦¤V = Isp * g0 * ln(m0/mf)

Where:
- ¦¤V is the required change in velocity
- Isp is the specific impulse of the propulsion system
- g0 is the standard gravitational acceleration (9.81m/s^2)
- m0 is the initial mass of the rocket (including propellant)
- mf is the final mass of the rocket (after the propellant is expended)

For both questions, we need to solve for the propellant fraction (m0 / mf). Rearranging the equation, we get:

m0 / mf = e^(¦¤V / (Isp * g0))

Now let's calculate the propellant fraction for each propulsion system:

Question 1:
For the cryogenic chemical propulsion system (Isp = 450s) with ¦¤V = 9.6km/s, we plug these values into the equation:

m0 / mf = e^(9.6km/s / (450s * 9.81m/s^2))
= e^(9600m / (450 * 9.81))
= e^(2.172)

Using a calculator or mathematical software, we find that e^(2.172) = 8.779.

Therefore, the propellant fraction required for the cryogenic chemical propulsion system is 8.779.

Question 2:
For the electric propulsion system (Isp = 2000s) with ¦¤V = 9.6km/s, we repeat the calculation:

m0 / mf = e^(9.6km/s / (2000s * 9.81m/s^2))
= e^(9600m / (2000 * 9.81))
= e^(4.915)

Using a calculator or mathematical software, we find that e^(4.915) = 136.06.

Therefore, the propellant fraction required for the electric propulsion system is 136.06.

Please note that the propellant fraction is a dimensionless proportion, so there is no unit associated with it.