Satellite mechanics: linear and rotational momentum

Thread starter vasya
Start date Nov 21, 2022
Tags

Classical mechanics Linear Mechanics Momentum Rotational Satellite

In summary, the conversation is discussing a question about a satellite with a thruster that ejects 100g of propellant with a speed of 1000m/s, giving the satellite a momentum of 100kg m/s. The question is how much of this momentum will be given to rotation and how much to linear motion. To answer this question, the concept of conservation of linear and angular momentum is brought up. The conversation then delves into the mathematical expressions for these conserved quantities and how they relate to the problem at hand. The importance of choosing a specific axis for calculating angular momentum is also mentioned. Overall, the goal is to guide the OP in understanding how to solve such problems rather than just providing the answer.

Dec 17, 2022

jbriggs444

Science Advisor

Homework Helper

vasya said:

look more closely on first picture in this thread. thruster has offset of 0.25m of y-piersing-through-the-center-of-mass axis

Thank you. That explains the factor of two discrepancy in our two evaluations for rotation rate.

<h2>1. What is the difference between linear and rotational momentum in satellite mechanics?</h2><p>Linear momentum refers to the motion of an object in a straight line, while rotational momentum refers to the motion of an object around a fixed point. In satellite mechanics, linear momentum is important for determining the trajectory and velocity of a satellite, while rotational momentum is important for maintaining the orientation and stability of the satellite.</p><h2>2. How is linear momentum conserved in satellite orbits?</h2><p>In satellite mechanics, linear momentum is conserved through the principle of conservation of angular momentum. This means that the total momentum of a satellite in orbit remains constant, even as it moves through different points in its orbit. This is due to the fact that there are no external forces acting on the satellite in space, so its momentum cannot change.</p><h2>3. What factors affect the rotational momentum of a satellite?</h2><p>The rotational momentum of a satellite is affected by its mass, shape, and the distribution of its mass. A larger and more massive satellite will have a greater rotational momentum, while a satellite with an irregular shape or uneven mass distribution will have a more complex rotational momentum.</p><h2>4. How does rotational momentum impact the stability of a satellite?</h2><p>In satellite mechanics, rotational momentum plays a crucial role in the stability of a satellite. If the rotational momentum is too high, the satellite may experience unwanted tumbling or spinning, which can disrupt its orbit and functionality. Therefore, it is important for engineers to carefully design and control the rotational momentum of a satellite to ensure its stability.</p><h2>5. Can satellite mechanics be used to predict and correct orbital anomalies?</h2><p>Yes, satellite mechanics can be used to predict and correct orbital anomalies such as changes in orbit or unexpected movements. By analyzing the linear and rotational momentum of a satellite, engineers can identify the cause of the anomaly and make adjustments to the satellite's trajectory or orientation to correct it. This is crucial for maintaining the functionality and safety of satellites in orbit.</p>

1. What is the difference between linear and rotational momentum in satellite mechanics?

Linear momentum refers to the motion of an object in a straight line, while rotational momentum refers to the motion of an object around a fixed point. In satellite mechanics, linear momentum is important for determining the trajectory and velocity of a satellite, while rotational momentum is important for maintaining the orientation and stability of the satellite.

2. How is linear momentum conserved in satellite orbits?

In satellite mechanics, linear momentum is conserved through the principle of conservation of angular momentum. This means that the total momentum of a satellite in orbit remains constant, even as it moves through different points in its orbit. This is due to the fact that there are no external forces acting on the satellite in space, so its momentum cannot change.

3. What factors affect the rotational momentum of a satellite?

The rotational momentum of a satellite is affected by its mass, shape, and the distribution of its mass. A larger and more massive satellite will have a greater rotational momentum, while a satellite with an irregular shape or uneven mass distribution will have a more complex rotational momentum.

4. How does rotational momentum impact the stability of a satellite?

In satellite mechanics, rotational momentum plays a crucial role in the stability of a satellite. If the rotational momentum is too high, the satellite may experience unwanted tumbling or spinning, which can disrupt its orbit and functionality. Therefore, it is important for engineers to carefully design and control the rotational momentum of a satellite to ensure its stability.

5. Can satellite mechanics be used to predict and correct orbital anomalies?

Yes, satellite mechanics can be used to predict and correct orbital anomalies such as changes in orbit or unexpected movements. By analyzing the linear and rotational momentum of a satellite, engineers can identify the cause of the anomaly and make adjustments to the satellite's trajectory or orientation to correct it. This is crucial for maintaining the functionality and safety of satellites in orbit.