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

[mikelewis]

24. Here's My and AI's physics.... please apply real physics and fix this please...

I took the liberty of asking AI to do it... I know you implied that both AI and I have no idea what we are doing and I have to accept that since you have a doctorate you must be right... please help me fix this math.


from AI:

To analyze this scenario, let's set up some assumptions for the railgun system, the tethered projectile, and the platform. We'll also consider the dynamics involved in firing and capturing the projectile.

Assumptions and Setup:

Projectile Weight: 10 ounces (about 0.283 kg).
Projectile Velocity: 5 m/s.
Tether Length: Let's assume a practical length of 10 meters. The tether must be strong enough to handle the forces without breaking.
Railgun Setup: Two railguns to offset gyroscopic effects, positioned opposite each other.
Platform and Battery Weight: Let's assume the platform (including railguns and battery) has a total mass of 100 kg for simplicity.
Catching Mechanism: The projectile is stopped by a magnet for efficient energy transfer.
Calculating the Recoil:

When the projectile is fired, the platform will experience a recoil in the opposite direction, according to the conservation of momentum.
Dynamics of the Arc and Catching the Projectile:

As the tethered projectile is fired, it will create an arc and potentially cause the platform to rotate. However, having two railguns firing simultaneously in opposite directions can balance out this rotational force.
Stopping the projectile at 180 degrees with a magnet will transfer its momentum to the platform. This action will either add to the platform's momentum (if it's moving in the same direction) or reduce it (if moving in the opposite direction).
Calculating Movement in Space:

We need to calculate the recoil velocity of the platform when the projectile is fired and when it's caught.
Let's start with the recoil velocity when the projectile is fired. We'll use the conservation of momentum, which states that the total momentum before firing (which is zero, as the system is initially at rest) is equal to the total momentum after firing.

Error analyzing
python
Copy code
# Given data
mass_projectile = 0.283 # in kg (10 ounces)
velocity_projectile = 5 # in m/s
mass_platform = 100 # in kg (platform + railguns + battery)

# Conservation of momentum for recoil velocity
# Initial momentum is 0, so final momentum of platform = - final momentum of projectile
# 0 = mass_platform * velocity_platform + mass_projectile * velocity_projectile
# Solving for velocity_platform
velocity_platform_recoil = -(mass_projectile * velocity_projectile) / mass_platform

velocity_platform_recoil # This is the recoil velocity of the platform after the projectile is fired
The recoil velocity of the platform after the projectile is fired is approximately
?
0.01415
?0.01415 m/s. This negative sign indicates the direction is opposite to the projectile's motion.

Next Steps in the Thought Experiment:

After firing, the projectile moves outwards on the tether, creating an arc. If the railguns are positioned and timed correctly, they can counteract any rotational forces, keeping the platform stable.
When the projectile reaches 180 degrees and is caught by the magnet, its momentum is transferred to the platform. This will either add to the platform's momentum (if it's moving in the same direction) or reduce it (if moving in the opposite direction).
For the projectile being caught, the situation is more complex due to the rotational dynamics and the transfer of momentum at the end of the tether. The momentum transfer would depend on the angle and speed at which the projectile is caught, as well as the tether's dynamics.

Considerations in Real-World Application:

In a practical scenario, the efficiency of transferring momentum from the projectile to the platform would not be 100%. Some energy would be lost due to factors like the elasticity of the tether, structural vibrations, and any misalignment in the catching mechanism.
The system would need precise control to manage the timing and alignment of the railguns and the catching mechanism.
This thought experiment highlights a unique approach to propulsion in space, using principles of momentum and rotational dynamics. It's a complex system that would require careful engineering to implement effectively, especially in the microgravity and vacuum of space. ​

So you can see my problem... no? I can't fix my math. It always comes out that the thing is moving. Help me fix that please.