# Is there a limit to the mass of a chemical rocket leaving for Earth orbit in a single stage?

Is there a limit to the mass of a chemical rocket leaving for earth orbit in a single stage?

Payload, fuel, structure ... all things considered.

• Leaving to get in the orbit of the earth or escaping from earth? – AHB Feb 2 '17 at 21:03
• – user140606 Feb 2 '17 at 21:08
• Practically (are there size limitations?), yes, but they're not given by the equation you cite. – Bill N Feb 2 '17 at 21:08
• For a rocket in the gravitational field of earth the important factor is the rate at which you burn fuel (source: Kleppner&Kolenkow An Introduction to Mechanics the chapter about momentum. Rocket motion section). – AHB Feb 2 '17 at 21:08
• Leaving to get into orbit. Good additional reading – Uzer Feb 2 '17 at 21:16

## 1 Answer

There is no hard limit to the mass, but practically speaking, for existing rocket fuels, $v_e\,\ln(\frac{m_0}{m_f})$ is limited to speeds well below escape velocity. Maximum fuel fractions are of the order of perhaps 98% or so, since you are going to need some mass for the structure of the rocket and its engines. You could achieve very high $v_e$ with non-chemical rockets, but those typically require a lot more structure. Bottom line is that at the current state of the art, you cannot really make it into orbit with a single-stage rocket, unless you have an air-breathing engine so you can take the oxidant part of your fuel from the atmosphere.