1
$\begingroup$

I am working on a project and i need the payload capabilities of different rockets to LEO, mars and lunar orbit. Usually the LEO payload along with all other relevant data is given for all rockets. is there any way i can calculate the other two from that?

$\endgroup$
1
0
$\begingroup$

Yes, there is and it's surprisingly easy!

First determine which target are you trying to reach, as it will alter the necessary trajectory. The most fuel-efficient trajectory, broadly speaking, is the Hohmann maneuver, however it is also the most time-consuming (you could travel faster, yet less fuel-efficiently; or use gravity assists for more efficiency and longer travel times).

To calculate payloads one can use Tsiolkovsky rocket equation, whose parameters are delta-V (total necessary change of velocity, which is constant for a given trajectory; specifically its geometry in 4-D space), $v_e$ - the exhaust velocity for the gas exiting rocket engine (relative to the rocket), and $m_0$ - the mass of the rocket itself (with all the cargo, crew etc; except fuel). In this example (see image) $m_{degvielai}$ is the mass of fuel (sorry for the index - it's in Latvian, as I took it from one of my older papers, which is also in Latvian; "degviela" in Latvian means "fuel")

Derived equation

And voila, that's how you calculate the required fuel. If you know the amount of fuel and the mass of the rocket with all its parts and want to calculate the payload, just reverse the expression and subtract the mass of the rocket from total initial mass.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.