KSP actually models this well; try putting something into a retrograde orbit and compare how easy it is compared to putting it into a regular orbit. If you fly both well, you'll have less left-over delta-v in the craft that you put into a retrograde orbit (if it makes it to orbit at all).
Alternatively, just switch to "orbital speed" on your navball while sitting on the launchpad. That's what you benefit from if you are launching west-to-east, but what you have to overcome if you launch into a retrograde orbit.
In Florida (28 degrees north) the earth surface travels at 400 m/s eastwards. (earth circumference * cos(28) / day)
A spacecraft that would launch from the ground and start westwards, would, after gaining the first 400 m/s relative to its starting point only be stationary relative to the earth's center. Then after 800 m/s, it would travel at 400 m/s westwards. Say if your orbital velocity is 8.0 km/s.
Your total delta vee would be 8.4 km/s.
In comparison, an eastward flying rocket would start from 0.4 km/s , and would need rocket propulsion only for the remaining 7.6 km/s. A 10% saving compared to the westward rocket!
In reality it's a bit more complex as you don't launch straight east or west anyway, and ISS is at a 50 degree inclination etc...
Exactly, and this is maximized by putting launch sites close to the equator. This is one reason why the European Space Agency launches from South America, by the way:
> Kourou lies at latitude 5°3', just over 500 km north of the equator. Its nearness to the equator makes it ideally placed for launches into geostationary transfer orbit as few changes have to be made to a satellite’s trajectory.
> Launchers also profit from the ‘slingshot’ effect, that is the energy created by the speed of the Earth’s rotation around the axis of the Poles. This increases the speed of a launcher by 460 m per second. These important factors save fuel and money, and prolong the active life of satellites.
When you next launch a rocket in KSP, click on the speed indicator right before or after take-off to switch it from "surface" to "orbital". You'll see that the rocket already has a horizontal velocity from the rotation of Kerbin, even before it starts accelerating.
> 1. You launch eastwards so you get the bonus speed from earth's rotation
Once the ship leaves the ground the earth's rotation has little to do with the flight except for landing location.
source: I play KSP