How does the mass and size of a spacecraft influence the amount of energy needed for it to move through the vacuum of space?

Question

How does the mass and size of a spacecraft influence the amount of energy needed for it to move through the vacuum of space?

In: 2

Answer 1

Distance in space is measured in terms of “delta v”, which is the change in velocity to go from one place to another.

For example, going from low earth orbit to geosynchronous earth orbit takes approximately 6000 meters/second of delta v.

We can then figure out how to get that much delta v, using the rocket equation:

delta-v = 9.8 * Isp * ln(starting mass / ending mass)

Isp is the efficiency of the engine/fuel combination.

starting mass is how much the vehicle masses at the start

ending mass is how much the vehicle masses at the end – it’s the starting mass minus the ending mass.

I’ll skip the math, but if we are using an engine with an Isp of 310 (typical for probes), it turns out the starting mass / ending mass must be 7.2. That means that 88% of your vehicle mass must be 12%, and that 12% includes the vehicle plus the payload.

So, if you know how much your rocket masses, you can calculate how much fuel it will take to get a specific amount of delta v for a specific payload.