A new means of space propulsion... closed loop pulse propulsion... here's the idea

[mikelewis]

73. AI's response

Your scenario involves a series of events in space involving railguns, projectiles, and conservation of momentum. Let's break down each event and analyze it based on the principles of physics:

Firing Railguns: When a railgun is fired, it exerts a force on the projectile, propelling it forward. By Newton's third law (action-reaction), the ship will experience an equal and opposite force, pushing it in the opposite direction of the projectile. If two railguns are fired, the effect doubles, assuming both railguns exert equal forces. Gyroscopic effects are indeed canceled out if the railguns are symmetrically aligned and fired simultaneously.

Projectile Entering an Arc: When the projectile is redirected into an arc, it does conserve its linear momentum initially. The conservation of angular momentum also applies if the projectile is made to move in a curved path, like an arc. However, the linear momentum of the projectile will change direction as it moves through the arc.

Redirecting Momentum: In space, without air resistance or other forces, a projectile can indeed have its momentum redirected. The tether can change the direction of the projectile's momentum, redirecting it 180 degrees. This is a result of the forces exerted by the tether on the projectile.

Catching the Projectile: Catching the projectile with a magnet and stopping it would transfer its momentum to whatever catches it. If the ship catches it, the momentum of the projectile is transferred to the ship. In space, forces can combine or be transferred, just like on Earth.

Now, regarding your specific questions:

Conservation of Linear Momentum in the Arc: The linear momentum is conserved in the sense that the momentum (mass times velocity) of the system (ship plus projectile) remains constant unless acted upon by external forces. When the projectile enters the arc, its direction changes, but the system's total momentum remains constant.

Subtracting Force with Same Direction Motion: If the projectile is traveling in the same direction as the ship and then collides with the ship, it doesn't "subtract" force. Instead, the momentum of the projectile is added to the ship's momentum. The resulting speed of the ship after this collision depends on the masses of the ship and the projectile and their velocities. If the projectile is much smaller than the ship, the change in the ship's speed will be small.

In summary, your scenario is largely consistent with the principles of physics. The key is understanding that momentum is conserved in an isolated system unless external forces are applied. Changes in the direction of momentum are possible with the application of forces, as with the tether redirecting the projectile.




User
So explain this to me... what exactly is happening step by step

2 / 2

ChatGPT
Certainly, let's break down your scenario step by step to understand the physics at play:

1. Firing the Railguns
Action: Two railguns on a spaceship are fired in the opposite direction to the ship's intended movement (direction B).
Physics Involved:
Conservation of Momentum: The momentum imparted to the projectiles by the railguns is equal and opposite to the momentum imparted to the ship. The ship moves in the opposite direction (direction A) due to the recoil.
Gyroscopic Effects: If the railguns are aligned symmetrically and fire simultaneously, any gyroscopic effects (which could cause the ship to spin) are canceled out.
2. Projectile Enters an Arc
Action: The projectiles, moving in direction B, enter a tethered arc mechanism.
Physics Involved:
Conservation of Linear Momentum: Initially, the linear momentum (the product of mass and velocity) of the projectiles is conserved. As they enter the arc, the direction of their momentum changes, but the magnitude remains constant.
Conservation of Angular Momentum: When the projectiles follow a curved path, angular momentum comes into play. The tether exerts a centripetal force, changing the direction of the projectiles' motion.
3. Redirecting Momentum
Action: The arc redirects the projectiles' motion by 180 degrees, now moving in the same direction as the ship (direction A).
Physics Involved:
Forces in Space: The tether, through tension, exerts a force on the projectiles, causing them to change direction. This is a central force causing a change in the direction of the velocity vector of the projectiles, but not necessarily their speed.
4. Catching the Projectile
Action: The projectiles, now moving in direction A, are caught and stopped by a magnet on the ship.
Physics Involved:
Momentum Transfer: When the ship catches the projectiles, their momentum is transferred to the ship. This is again an action-reaction pair. The force exerted by the magnet on the projectile is equal and opposite to the force exerted by the projectile on the magnet (and hence the ship).
Analysis of the Questions:
Conservation of Linear Momentum in the Arc:
When the projectiles enter the arc, their linear momentum's direction is altered, but the momentum's magnitude remains the same. The system (ship + projectiles) conserves total momentum unless acted upon by an external force.
Projectile and Ship Moving in the Same Direction:
When the projectiles, now moving in the same direction as the ship, are caught, their momentum adds to that of the ship. This doesn't negate the forces; it combines them. If the projectiles are significantly lighter than the ship, the effect on the ship's velocity might be minor, but it is still an addition of momentum, not a subtraction.
In summary, your scenario demonstrates various applications of Newton's laws of motion, particularly the conservation of linear and angular momentum, in a space environment where external forces are minimal.

User
Ok... can you break this down into parts... what sections of math do I need to use and where?
ChatGPT
Certainly! Breaking down your scenario into its physical components and identifying the relevant sections of math will help clarify how to approach the problem. Here's how you can categorize and apply mathematical concepts to each part of the scenario:

1. Firing the Railguns
Relevant Math:
Newton's Second Law (F = ma): To calculate the force exerted by the railguns.
Momentum (p = mv): To determine the momentum imparted to both the projectile and the ship.
Conservation of Momentum: To understand how the ship's velocity changes due to the firing of the railguns.
Application:
Calculate the momentum imparted to the projectiles.
Apply conservation of momentum to find the recoil velocity of the ship.
2. Projectile Enters an Arc
Relevant Math:
Conservation of Linear Momentum: To analyze the change in direction of the projectile's momentum.
Circular Motion Equations: For calculating the forces and velocities while the projectile is in the tethered arc.
Centripetal Force (F = mv²/r): To determine the force exerted by the tether.
Application:
Use circular motion equations to analyze the motion of the projectile in the arc.
Apply conservation of linear momentum to understand how the overall momentum of the system remains constant.
3. Redirecting Momentum
Relevant Math:
Vector Addition: To understand how the direction of the projectile's momentum changes.
Application:
Use vector addition to analyze the change in the direction of the projectile’s momentum as it is redirected by the arc.
4. Catching the Projectile
Relevant Math:
Conservation of Momentum: To determine how the momentum of the projectile is transferred to the ship.
Impulse (J = Ft): To calculate the change in momentum as the projectile is caught.
Application:
Apply conservation of momentum to find the final velocity of the ship after catching the projectile.
Use impulse-momentum theorem if the time of impact is considered.
General Considerations
Algebra and Calculus: For general problem-solving, setting up equations, and solving for unknowns.
Vector Analysis: Since forces and velocities are directional quantities, vector analysis is crucial in all parts.
Steps to Approach the Problem
Define Variables: Masses, velocities, forces, time durations, etc.
Set Up Equations: Based on the physics principles mentioned above.
Solve Sequentially: Each part of the scenario affects the next, so solve in the order of events.
Check Units and Consistency: Ensure that all units are consistent and calculations make physical sense.
By applying these mathematical principles to each part of the scenario, you'll be able to quantitatively analyze the situation and understand the physics behind each step.

User
So does the arc remove the momentum from the initial firing and why?
ChatGPT
The arc does not remove the momentum from the initial firing, but it does alter the direction of the momentum. Let's clarify why this is the case:

Conservation of Momentum: Momentum is a vector quantity, meaning it has both magnitude and direction. In an isolated system (one not affected by external forces), the total momentum remains constant. This is known as the conservation of momentum.

Initial Firing of the Railguns: When the railguns fire, they impart a certain momentum to the projectiles (in one direction) and an equal and opposite momentum to the ship (in the opposite direction). This is an application of Newton's third law of motion (action and reaction are equal and opposite).

Projectile Entering the Arc: When the projectile enters the arc, the direction of its momentum changes. The arc effectively acts as a force that redirects the projectile. The magnitude of the linear momentum of the projectile is conserved initially (ignoring any minor forces such as friction from the tether), but its direction is altered.

Effect of the Arc on Momentum:

Change in Direction: The arc changes the direction of the projectile's momentum, but not its magnitude.
Conservation Law: The conservation of linear momentum still holds, but since the direction changes, the vector sum of the momentum of the system (projectile + ship) will be different after the projectile has been redirected.
No Removal of Momentum: The arc does not remove momentum from the system; it merely redirects it.
Angular Momentum: When the projectile moves in a curve (due to the arc), it also has angular momentum (which is a different concept from linear momentum). The conservation of angular momentum would apply to the motion of the projectile around the arc, considering the pivot point of the arc as the center.

Catching the Projectile: Finally, when the ship catches the projectile, the momentum of the projectile is transferred to the ship. This again follows the conservation of momentum.

In summary, the arc in your scenario does not remove the momentum generated by the initial firing of the railguns. It changes the direction of the projectile's momentum. The total linear momentum (in terms of magnitude and direction) of the ship-projectile system is conserved throughout the process, in accordance with the law of conservation of momentum.


2 / 2

User
Why doesn't the projectile cancel out the momentum and drag the ship back into place. So here's the problem... you shoot... the spaceship starts to move... and that projectile has to drag it back into place... how does it do that?
ChatGPT
In your scenario, the idea that the projectile, once redirected and caught by the ship, would "drag" the ship back to its original position involves a few misconceptions about momentum and how it works in space. Let's clarify these points:

1. Initial Firing of the Railguns
What Happens: When the railguns fire, the ship gains momentum in one direction (let's say, direction A) due to the recoil, and the projectiles gain an equal amount of momentum in the opposite direction (direction B).
Physics Principle: This is an application of the conservation of momentum. The total momentum of the system (ship + projectiles) remains constant.
2. Redirecting the Projectile
What Happens: The projectile's direction of motion is changed by the arc, but this does not change the total momentum of the system.
Physics Principle: The redirection alters the direction of the projectile's momentum but not its magnitude (assuming no external forces). The ship, meanwhile, continues moving in its original direction unless acted upon by another force.
3. Catching the Projectile
What Happens: When the ship catches the projectile, the projectile's momentum is transferred to the ship.
Misconception: The projectile does not "drag" the ship back to its original position. Instead, the momentum of the projectile is added to the momentum of the ship.
Physics Principle: The ship's momentum after catching the projectile is the vector sum of its own momentum and the projectile's momentum.
Why the Ship Doesn't Return to Its Original Position
No Canceling Out: The momentum of the projectile, once it's redirected and caught by the ship, doesn't cancel out the ship's initial momentum. Instead, it adds to it.
Vector Summation: The final momentum of the ship is a vector sum of its initial momentum and the momentum of the projectile.
Space Environment: In space, there's no friction or other force to naturally stop or reverse the ship's motion. The ship will continue moving unless an equal and opposite force is applied to negate its momentum.
Summary
Conservation of Momentum: The key principle here is the conservation of momentum. The total momentum of the system (ship + projectiles) remains constant unless an external force acts on it.
Direction and Magnitude: While the direction of the projectile's momentum changes, this redirection and subsequent catching by the ship do not bring the ship back to its original position. They merely change the total momentum of the ship.
In essence, once the ship has started moving due to the firing of the railguns, it will not return to its original position simply by catching the projectile. The overall momentum of the ship will be altered by the momentum of the caught projectile, but not necessarily negated.

User
But if they are caught in the same direction... if the projectile and the ship collide in the same direction?
ChatGPT
If the projectile and the ship collide (or the projectile is caught) while moving in the same direction, the result will still not bring the ship back to its original position, but it will affect the ship's speed. Let's explore what happens in this scenario:

Collision/Catching in the Same Direction
Scenario: The ship fires the projectile, gains momentum in one direction (let's say forward), and then the projectile is redirected (via the arc) to move in the same direction as the ship. Finally, the ship catches or collides with the projectile.

Momentum Transfer: When the ship catches or collides with the projectile, the momentum of the projectile is transferred to the ship. Since both are moving in the same direction when this happens, their momenta are additive.

Effect on the Ship's Velocity:

The ship's velocity will change based on the combined momentum of the ship and the projectile.
If the mass of the projectile is much smaller than the mass of the ship, this change might be relatively small.
The direction of the ship's motion will not change, only its speed.
Calculating the Resulting Velocity
To calculate the resulting velocity of the ship after catching the projectile, we can use the conservation of momentum. The total momentum before and after the collision remains the same. The formula is:
### Calculating the Resulting Velocity

To calculate the resulting velocity of the ship after catching the projectile, we can use the conservation of momentum. The total momentum before and after the collision remains the same. The formula is:

[ m_{text{ship}} cdot v_{text{ship, initial}} + m_{text{projectile}} cdot v_{text{projectile}} = (m_{text{ship}} + m_{text{projectile}}) cdot v_{text{final}} ]

Where:
- ( m_{text{ship}} ) is the mass of the ship.
- ( v_{text{ship, initial}} ) is the initial velocity of the ship.
- ( m_{text{projectile}} ) is the mass of the projectile.
- ( v_{text{projectile}} ) is the velocity of the projectile.
- ( v_{text{final}} ) is the final velocity of the ship after catching the projectile.

### Summary

- **No Return to Original Position**: Catching the projectile does not reverse the ship's initial motion or bring it back to its original position.
- **Change in Speed**: The ship's speed will change depending on the momentum of the projectile. The direction of motion remains the same.
- **Conservation of Momentum**: This scenario still follows the principle of conservation of momentum. The total momentum of the system (ship + projectile) before and after the collision remains constant.

In conclusion, in space, without external forces, catching the projectile in the same direction as the ship is moving will only alter the ship's speed, not bring it back to its original position.
is the final velocity of the ship after catching the projectile.
Summary
No Return to Original Position: Catching the projectile does not reverse the ship's initial motion or bring it back to its original position.
Change in Speed: The ship's speed will change depending on the momentum of the projectile. The direction of motion remains the same.
Conservation of Momentum: This scenario still follows the principle of conservation of momentum. The total momentum of the system (ship + projectile) before and after the collision remains constant.
In conclusion, in space, without external forces, catching the projectile in the same direction as the ship is moving will only alter the ship's speed, not bring it back to its original position.