Fundamental limits of rocket launch to orbit around Earth

The only technologically feasible way to launch rocket, spaceship, spacecraft into the space presently is using reactive engine.


The operation principle of reactive engine.
Reactive engines operate on the principle of momentum conservation. In ideal world, if the first object with mass m1 and velocity v1 hits the second object and stops abruptly, the second object will absorb the kinetic energy of the first object and will continue travel with the same velocity v2=v1 if the masses of both objects are equal m1 = m2.

The same happens when the the object is split into 2 equal objects and if the first moves away with velocity v1, the other one will move to the opposite direction with velocity v2 = v1.
To continue acceleration, the rocket must eject its mass continuously at as large velocity as possible, hence becoming lighter with time.

The equation describing fundamental maximum velocity the rocket can reach:
Delta-v = v_e * ln(m_initial / m_final).
https://en.wikipedia.org/wiki/Spacecraft_propulsion#Delta-v_and_propellant
In practice, due to several types of inefficiencies, the Delta-v will be less then fundamental maximum.
Lets express for m_initial = m_final * exp(Delta-v/v_e),

What is the required minimal mass for a spacecraft to lift the human up in circular orbit around Earth?
Mass of human, m_final = 100 kg
https://en.wikipedia.org/wiki/De_Laval_nozzle#Exhaust_gas_velocity
v_gas = 3000 m/s.

Total mechanical energy of the orbiting satellite E = K+U = - G*M*m/2r = 1/2 m*v^2, M and m are masses of Earth and satellite respectively.
v = sqrt(G*M/r).
Velocity of a spacecraft in a circular 100 km orbit is:
v = sqrt(6.67e-11 N*m2/kg^2 * 5.98e24 kg / (6.37e6 m + 300e3 m)) = 7.85 km/s.
Lets assume Delta-v ~= 8 km/s.

Then, m_initial = 100 * e^(8e3/3000) = 1.44e3 kg = 1400 kg.
This is a minimum fundamental weight required for a rocket which is propelled by the reaction engine to carry a human into an orbit around Earth.

What is required fundamental minimum rocket's acceleration for it to reach circular orbit around Earth?
a_initial = Thrust / M_rocket_initial = Fuel_burn_rate*v_gas / M_rocket_initial > 9.8 m/s2.
What is the minimum required fuel burn rate in rocket's reactive engine?
Fuel_burn_rate > 9.8 * M_rocket_initial / v_gas
Fuel_burn_rate > 9.8 * 1000 / 3000 > 3.3 kg/s.

Reaction engine can eject the mass at high velocities due to:
a) energy provided by chemical or nuclear reaction.
b) energy provided by external laser from outside of the rocket.
Laser propulsion is awesome, because fundamentally one can heat up any matter, including air. For the future launches this is important because of global warming or launching from the planets without specific chemical resources or atmosphere (eg. Moon).
Assuming the laser must hit the rocket within the area of 10m in diameter, and the rocket is traveling with velocities around 8000 m/s, laser controls need to have 10/8000 ~= 1ms precision, otherwise laser beams will either miss the rocket completely or will burn the payload.
A feedback would make aiming the laser beam into the target area on the rocket. Assuming the orbit distance from Earth 1000km, speed of light is 3e8 m/s, the minimum fundamental time it takes for the rocket to communicate with the laser station is 1e6/3e8 = 3e-3 s = 3ms.
Due to laser divergence there will be a fundamental limit for a distance that the laser propulsion will be effective.