Using the following engine parameters, calculate the chamber pressure:

• c* = 1800 m/s (Characteristic velocity)
• Mass flow rate: 1500 kg/s 
• Thrust coefficient: 1.8 
• Throat area: 0.6 m² 
• g0 = 9.81 m/s² 

Using the following engine parameters, calculate the chamber pressure:

• c* = 1800 m/s (Characteristic velocity)
• Mass flow rate: 1500 kg/s 
• Thrust coefficient: 1.8 
• Throat area: 0.6 m² 
• g0 = 9.81 m/s² 

Please see the attached image about the Space Shuttle Endeavour. What would be the positive yaw angle (Y+, orange arrow, rotation on XY plane) turned by the Space Shuttle orbiter in 5 seconds if we fire thruster F5L (yellow vector) for 1 second? Thruster F5L features a 60 deg angle with the XY plane and the thrust vector application point falls 10 meters away from the center of mass (normal distance).

Consider the space shuttle as a cylinder, 80 tons mass and 2 meter radius . g = 9.81 m/s. Thruster F5L has a 310 sec specific impulse and mass flow 0.65 kg /sec. The spaceship is initially at rest and in space.

A spacecraft is in a heliocentric orbit trailing Earth. It is desired to perform a Hohmann transfer maneuver to enter a heliocentric orbit trailing Mars. Calculate the required propellant mass for this operation. The spacecraft has a dry mass of 5000 kg (excluding propellant for this maneuver) and an engine with an exhaust velocity of 4.4 km/s.

(Heliocentric trailing orbit means that this spacecraft is close to and trailing Earth or Mars, but actually orbiting the Sun, not these planets).

• μ Sun = 1.327 × 10E20 m3 / s2
• Earth's orbital radius = 1 AU
• Mars' orbital radius = 1.52 AU

Arrakis presents a unique challenge with its different atmospheric pressure regarding Caladan (your original planet). This could significantly affect the performance of your frigates' rocket engines, designed initially for Caladan. Your task is to analyze the engine's performance under these new conditions.

Given the following engine parameters, determine the nozzle conditions and Specific Impulse. The success of the spice mining operation, and perhaps the fate of House Atreides, rests on your calculations.

Engine Parameters:

• Chamber pressure = 14.6 Mpa
• Chamber temperature = 4250 K
• Gas constant = 360 J/(kg K)
• Specific heat ratio; gamma = 1.3  
• Ambient pressure  = 71320 Pa
• Nozzle expansion ratio = 15  
• Exit diameter = 2.1 m
• Mass flow rate = 3100 kg/s 
• g0 = 9.81 m/s² (Arrakis gravity is very close to Earth's)

The ASM-135 ASAT (Anti-Satellite) was a US missile system designed to destroy satellites in low Earth orbit. It was developed by Ling-Temco-Vought Aerospace in the 1980s. This system was launched from a F-15A fighter in a near vertical zoom climb (see attached picture) and destroyed satellites by directly colliding with them at high speed ("kinetic kill"). This technology was only tested once at prototype stage and never entered production or seen real life use. 

We want to obtain the Thrust to Weight (T2W) ratio for the first stage of this missile system (initial T2W, take the initial missile mass). 

Parameters for this first stage:

• Initial velocity of the F-15 launch platform : 750 km/h
• Final velocity of the ASM-135 missile at the end of the 1st stage burn: 4500 km/h
• Initial mass of the missile : 1500 kg
• Final mass of the missile after 1st stage burn: 500 kg
• Acceleration due to gravity : 9.81 m/s²
• Burn time of the missile's rocket motor : 15 s

Suppose a vertical launch and trajectory and take into account the gravity pull on the missile. 

(These values are made up for this test, they may not be the same as for the real ASM-135)

Using the following engine parameters, calculate the chamber pressure:

• c* = 1800 m/s (Characteristic velocity)
• Mass flow rate: 1500 kg/s 
• Thrust coefficient: 1.8 
• Throat area: 0.6 m² 
• g0 = 9.81 m/s² 

As you should know at this point, the United Federation of Planets has an ongoing mission of discovering new worlds, to seek out new lifeforms and new civilizations, to boldly go where no one has gone before.

However, due to a shortage of dilithium, Starfleet Command has grounded the fleet. We must launch our ships using conventional old chemical rockets from the 21st Century.

You are the Chief Engineer on duty today. You have access to a 3-stage heavy launch vehicle with a Total Launch Mass of 65,000,000 kg (limited by the structural integrity of the launch pad).

Based on the engines efficiency and Delta V requirements, your science officer Spock has already calculated the payload ratios (lambda) for each stage as follows:

• Stage 3 (Final stage): λ_3 = 0.281

• Stage 2 (Intermediate): λ_2 = 0.238

• Stage 1 (Liftoff): λ_1 = 0.155

Task: Calculate the maximum payload capacity of this vehicle. Based on your result, which ship can you successfully deliver to a space injection trajectory?

- USS Enterprise, Constitution class, 1 million kg.

- USS Voyager, Intrepid class, 510,000 kg

- USS Defiant, Defiant class, 355,000 kg

Arrakis presents a unique challenge with its different atmospheric pressure regarding Caladan (your original planet). This could significantly affect the performance of your frigates' rocket engines, designed initially for Caladan. Your task is to analyze the engine's performance under these new conditions.

Given the following engine parameters, determine the nozzle conditions and Specific Impulse. The success of the spice mining operation, and perhaps the fate of House Atreides, rests on your calculations.

Engine Parameters:

• Chamber pressure = 14.6 Mpa
• Chamber temperature = 4250 K
• Gas constant = 360 J/(kg K)
• Specific heat ratio; gamma = 1.3  
• Ambient pressure  = 71320 Pa
• Nozzle expansion ratio = 15  
• Exit diameter = 2.1 m
• Mass flow rate = 3100 kg/s 
• g0 = 9.81 m/s² (Arrakis gravity is very close to Earth's)

A short-range ballistic rocket is launched at an angle of 60 degrees with the following initial parameters:

• g0: 9.81 m/s² (Acceleration due to gravity, constant)
• m0: 500 kg (Initial mass)
• mp: 100 kg (Propellant mass)
• Is: 250 s (Specific impulse)
• tp: 5.0 s (Burn time)

Calculate the norm value of the acceleration  vector of the rocket immediately after engine cut-off.

Note: Neglect air resistance and assume constant thrust throughout the burn phase.