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

[mikelewis]

32. I ask AI to review that statement... this is the response...

Your explanation touches on some important concepts in physics, particularly relating to angular momentum and centripetal force. Let's break down and clarify these ideas:

Centripetal Force and Angular Momentum:

Centripetal Force Formula: The formula
�
=
�
�
2
�
F=
r
mv
2

​
describes the centripetal force, where
�
m is mass,
�
v is the velocity of the object moving in a circle, and
�
r is the radius of the circle. This force is what keeps an object moving in a circular path.
Angular Momentum Conservation: In a system with no external torques, angular momentum is conserved. Angular momentum depends on the object's mass, its velocity (specifically its tangential velocity), and the distance to the axis of rotation (radius). The formula for angular momentum in circular motion is
�
=
�
�
�
L=mvr.
Figure Skaters and Angular Momentum:

When figure skaters pull their arms in, they reduce the radius
�
r of their rotation. Since angular momentum
�
L must be conserved (assuming no external torques), and
�
=
�
�
�
L=mvr, reducing
�
r means
�
v (the rotational velocity) must increase. This is why skaters spin faster with their arms pulled in.
Effect on Velocity:

Your point about the velocity changing and being squared in the centripetal force formula is crucial. As the radius changes, the velocity changes inversely to conserve angular momentum. The square of the velocity in the formula compensates for changes in the radius, ensuring that the force needed for circular motion is balanced with the system's energy.
Application to Your Scenario:

In the scenario with the tethered projectile, as it arcs, the direction of the force exerted on the astronaut (or platform) changes. This change is a result of the projectile's circular motion.
The energy considerations you mentioned come into play with the centripetal force needed to keep the projectile moving in its path. As the projectile moves out on the tether, the radius of its motion increases, which affects the velocity required to maintain its circular path.
Your explanation is on the right track in understanding the interplay of forces, motion, and energy in a rotating system. The key aspect here is the conservation of angular momentum and how changes in the radius of rotation affect the velocity and force required to maintain circular motion. The "magic" you refer to is the balance of these factors, ensuring that the physical laws, like the conservation of angular momentum, are upheld.