No. That is Newton's 2nd Law F=MA. Come on! You should know no one refers to the F=ma as the rocket equation!
From the start, it was always about the Rocket Equation. i.e. Tsiolkovsky's Rocket Equation.
You yourself has put out this equation earlier at the very start. Here,
" delta V [final] =V[exhaust speed] *ln(launch_mass/empty_mass)"
I have no clue what you want to say here.
The rockets working on a simple principle: they accelerate M.exhaust mass to V. exhaust, and it accelerate the rocket weighting M.rocket by a.rocket.
means there is two balancing force, the engine "pushing"force against the rocket inertia.
So, you can either calculate the engine force by using the acceleration of reactive mass and the mass flow, OR you can use the speed change of the rocket and the mass of rocket ( this is actually beyond the high school level if anyone wants it precisely )
Where did you get this kind of ridiculous simplistic calculation? The NEAs has a heliocentric orbit.
You can't do the calculation as if the NEA is orbiting Earth only. Even so, I don't see what this calculation is about!
This math of yours is just baloney. Give me break.
The earth escape velocity is 11 186 meters / seconds.
It calculated from the surface of earth ( sea level) , and means that if you accelerate on object horizontally on a rail ( with 0 air friction) by this mach it will enter a heliocentric orbit .
Now, to enter low level orbit takes 7800 meter/sec from sea level. By accelerating this much you enter a few hundred km height orbit around earth.
So, if you came back from the solar system then 3386 km/sec to go back to LEO.
However this is nonsense from the startin point of the topics, considering if you bring back mass from moon, then you have to d othe next to came back leo:
(moon surface-orbit)+(orbit-earth transfer)+(earth transfer-LEO)
The (moon surface-orbit) on its own 2.4 km/sec.
The NEA-LEO looks like
(solar orbit-earth capture) + (earth capture-LEO) .
The first leg in this case is 0.382 km/sec.
So, is it make sense to mine on moon?
No, you are the one who made the following "mistakes".
1. Your first mistake is to claim that NEA has the ridiculous LEO-to-NEA Delta-V value of 382 m/s when the bulk of them has around a 7 km/s value.
2. Your second mistake is your narrow view that a trip from the NEO --> Lagrange Point is
all there is to it, when it always has to be round trip. (You have to bring back the raw material, remember?)
1. LEO --> NEA --> LEO
or,
2. (Going through the NEA-to-LPt way) LEO --> LPt --> NEA --> LPt --> LEO.
But you only focused on the "NEA --> LPt" part!
i.e. The lower energy capture part! (Low Delta-V gravity capture, which is not always low energy, by the way, depending on the transfer orbit and the NEA heliocentric orbit)
That's why it seems so magical to you!
Remember, the Delta-V for LPt --> NEA can be even higher than LEO --> NEA , depending on the heliocentric orbit of the NEA.
When you consider the complete round trip the saving in energy is not that much, or even higher, with the cost of a more complicated maneuver i.e. the addition of LPt --> NEA --> LPt.
Wow, you never give up, don't you, despite the few articles I posted showing you're dead wrong on this opinion.
Again, the 7km/sec is from LEO orbit,but those are way beyond the Mars.
You can not do industrial activity on LEO, and even on medium earth orbit.
Due to tidal forces ( or the dramatic speed differences between close orbits) you can not put two object in close proximity without continuous propellant consumption, and example in LOE orbit the force in a tether between two objects separated by 100 km will be extremely high.
Additionally there is air drag.
IT will be in the range of 0.1 m/sec^2, if you calculate the force on 100 tons then the tether will be very heavy on its own.
Means there is no chance to use example solar furnaces.
So, if anyone want to make space industry the natural point of that is the L4/5 point.
It is cheap to bring back thing from the solar system, it is stable, and generally it require small and light structures to keep together a big and complicated structure.
Wow, you never give up, don't you, despite the few articles I posted showing you're dead wrong on this opinion.
Bring equations.
Similar like the one that I scanned for you from my notebook : )
I suggest to start with deltaV requirement for LEO-L4/5-NEA, rocket force calculation, tidal force calculation for LEO objects,NEQ- L4/5 capture orbit calculation.
Or it can be interesting if you can calculate the moon mining delta Vs with required fuel mass as well. Just to compare .
Connections / reasons / orbit differences, masses , effect on exhaust speed and time, hohmann transfer and so on.
IF you really on the top I can be interested if you can calculate same NEA - L4/5 low energy capture orbit. That require sophisticated math .
Don't forget, it is not "social science". bring the math. Show solved equations .