Question B: Interplanetary Cruise (Ungraded)

This problem follows Question A but can be done independently. Your spacecraft can be approximated by a cube (2x2x2 m, mass = 3000 kg). It is composed of 24 attitude thrusters (2 N each) and one powerful main engine. The main engine is perpendicular to one of the faces of the cube, and each face has 4 attitude thrusters (depicted as red arrows in the next figure).

You want to prepare your spacecraft for the maneuvers needed upon reaching Mars. To do so, you need to rotate the spacecraft by 180 degrees. For that rotation, you will use attitude thrusters per burn.

1. What is the minimum total maneuver time (in seconds) to slew the spacecraft by 180°? (Assume the center of mass is in the middle of the cube.)

2. What will be its temperature (in Celsius) when reaching Mars, knowing that only one of its faces is illuminated by the Sun and that the heat flow is homogeneously distributed? (The spacecraft is covered with black epoxy.)

3. How much power (in watts) should be dissipated inside the spacecraft to achieve 0°C? (Power generated inside the spacecraft can be considered as input power for the radiation balance.)

4. If you can't achieve that power dissipation on board, you could typically choose another coating. What property should it have? (Choose all correct answers.)
- Increased
- Increased
- Decreased
- Decreased

Question

16-09-2023
Engineering

College

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Question B: Interplanetary Cruise (Ungraded)

This problem follows Question A but can be done independently. Your spacecraft can be approximated by a cube (2x2x2 m, mass = 3000 kg). It is composed of 24 attitude thrusters (2 N each) and one powerful main engine. The main engine is perpendicular to one of the faces of the cube, and each face has 4 attitude thrusters (depicted as red arrows in the next figure).

You want to prepare your spacecraft for the maneuvers needed upon reaching Mars. To do so, you need to rotate the spacecraft by 180 degrees. For that rotation, you will use attitude thrusters per burn.

1. What is the minimum total maneuver time (in seconds) to slew the spacecraft by 180°? (Assume the center of mass is in the middle of the cube.)

2. What will be its temperature (in Celsius) when reaching Mars, knowing that only one of its faces is illuminated by the Sun and that the heat flow is homogeneously distributed? (The spacecraft is covered with black epoxy.)

3. How much power (in watts) should be dissipated inside the spacecraft to achieve 0°C? (Power generated inside the spacecraft can be considered as input power for the radiation balance.)

4. If you can't achieve that power dissipation on board, you could typically choose another coating. What property should it have? (Choose all correct answers.)
- Increased
- Increased
- Decreased
- Decreased

Answer :

Final answer:

The spacecraft's rotational maneuver duration is based on the total torque produced by the attitude thrusters and the spacecraft's rotational inertia. The temperature of the spacecraft when reaching Mars depends on solar absorption and radiation, determined by factors like distance from the Sun and properties of the outer coating. If the spacecraft can't maintain the desired temperature, alternate coatings with high reflectivity and low emissivity could be selected.

Explanation:

Considering the spacecraft forms a cube, the rotational inertia (I) can be computed using the formula I = 2/3 * Mass * Side_Length^2. Given the mass is 3000kg and the side length is 2m, thus the value of I will be 8000 kg*m^2. The thrust to rotate the spacecraft is provided by the attitude thrusters at the 4 corners, hence the total torque (τ) from each attitude thruster is equal to Thrust_force * Side_Length/2, with the four thrusters providing 4*τ. Rotational acceleration (α) can be derived using the formula τ = I*α, and hence time (t) can be computed as t=180° / α in seconds.

With regard to the spacecraft's temperature reaching Mars, it would depend on various aspects including the distance from the Sun, the spacecraft's surface area, solar constant, Stefan's constant, and the absorptivity and emissivity of the black epoxy coating. The equilibrium temperature can be calculated by equating the absorbed solar energy and the radiated energy, hence providing the spacecraft's temperature in Celsius.

The power dissipation required within the spacecraft can also be determined from the equations of thermal equilibrium. If the desired temperature is 0°C, the spacecraft needs to internally generate and dissipate a calculated amount of power to balance the temperature.

If the necessary power dissipation cannot be fulfilled, choosing a spacecraft coating with alternate properties is an option. In particular, low emissivity and high reflectivity would be desirable to minimize heat absorption and maximize reflection.

Learn more about Spacecraft Maneuvering and Temperature Balance here:

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Answer :

Final answer:

Explanation:

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