We can think of a rotating space tether around the moon like a big wheel.  The lets say the tether is 55 km but
the ballast is 5 km from the center of mass and the tip end is 50,000 m from the center of mass.
The tether is rotating like a spoke on a 50,000 m radius wheel.   If the center of mass is orbiting
at 1,600  m/s and the tip is rotating the other way at 1,600 m/s then when the tether is straight
down near the moon the tip will be momentarily stationary relative to the moon.

For this let us pretend the tip will momentarily touch a spot 100 meters above the surface of the moon 
at a spot we will call the rendezvous spot.

Please calculate the speed of the tip relative to the moon and distance from the landing
zone in the 12 seconds counting down to when the tip touches the landing zone at time 0.  
Please make a table with 0.2 second increments.




Also imagine we have a spring powered launcher that throws a payload from a spot on the moon's surface
that we will call the launch spot up 100 meters so it just has enough speed to get to the rendezvous spot and then comes to 
a stop.   Please make a table showing the payload speed and distance from the rendezvous
spot counting down from 12 seconds before rendezvous to rendezvous at time 0 in 0.2 second increments.
Also mention how long ahead of rendezvous time the launcher needs to launch.


Please make sure that time t=0 is the same on both tables so the payload and the tip are
rendezvous spot and the same time and distances and speeds at earlier times can be compared
between the two tables.



Also look at the question of how quickly we could raise or lower the tether tip.  
Lets say the tether weighs
100 kg and is made of Spectra.    The mobile ballast is 300 kg and has 10 hp electric motor for climbing
up and down the tether.  If the ballast pulls up on the tether the force propagates down the tether
at the speed of sound in the tether (faster than in air) so takes some time.  The motor has limited
power.  Try to estimate how much the tip could be pulled up or down in 1 to 20 seconds in 1 second
increments.  Note that if it takes more than 2 seconds for any pull on the tether to popagate
to the other end then in the first 2 seconds I want the table to show 0 meters of adjustment are possible.

Please write up the questions and answers such that a person interested in tethers could understand
the point of what we are doing and output everything in html so I can use it on a website.