Rocket equation :
Final speed = exhaust mass speed* natural
logarithm (1/(1-((fuel mass + oxidizer mass) / Total mass of the
(Exhaust masses speed is around 3500 to 4500 m/sec at best)
So to go to orbital speed (8000~m/sec) natural logarithm (1/(1-((fuel mass + oxidizer mass) / Total mass of the rocket))) must be at least 2.5.
This mean that ((fuel mass + oxidizer mass) / Total mass of the rocket) is around 0.1, which is impossible. No structure car be so light with current technology, and don't think rocket engineer have not work hard, some rockets are so light that the structure can stand only because of the internal pressure!
No need to say that SSTO are not for tomorrow...
Energy to lift a payload on LEO
The energy that must be used to lift a payload with a rocket on LEO is incredibly high.
At the same time there is enough energy in one kilogram of kerosene and oxidizer to lift it and a fraction more to LEO! The problem is that fraction is really small and to lift some tons of payload, you must use hundreds of tons of fuel and oxidizer!
The main motor on Space Shuttle (there is three one) produce 2.2 million newtons of thrust for a ISP of 455 seconds.
So it's: P = 2.2e+6 * 455 * 4.91 ~ 5 * 10^9 watts
It's equivalent to an electrical power plant for a one million inhabitants town.
This is because of :
One rocket must at least produce a thrust equal to is weight.
A rocket must push the payload, the structure and the fuel and oxidizer not already used.
A rocket must pass through atmosphere at either :
High speed and high drag
Low speed and high use of fuel and oxidiser to counter gravity.
Don't argue with me about that, make math!
The best thing is to use a spreadsheet to build a model, like :
Excel Simulation of a one stage rocket going to LEO
If you want to get a glimpse through an Internet simplified simulator go to my simple Rocket simulator
Thrust to weight ratio
Depending of the material used as energy container, the thrust to weight ratio is :
1. Chemical rockets :
Highest Thrust to weight: 50 to 1.
The chemical energy of inter atomic or molecular link is smaller per unit of mass than intra atom or nucleus link energy.
2. Nuclear thermal engines (very compact high
temperature reactors are possible, the high temperature giving high
exhaust speed see Molecules speed)
Highest Thrust to weight: 6 to 1.
(nobody is ready to authorize again this forbidden kind of rocket since the international agreement against the use of atomic form of energy in space in the 80')
So the best technology today is still the chemical rocket technology.