When launching a deep-space craft, how do the rotation and orbit speeds of the Earth and direction (relative to the prior) impact the travel time and actual velocity of the space craft?

Question

To simplify it for my mind, I envision the Earth being a car, and the space craft being something like a bullet. If the car (Earth) is orbiting at 30,000 m/s, and the bullet (spacecraft) is traveling at 17,000 m/s (Voyager 1 speed), the bullet is then traveling at 47km/s, but only at 17km/s relative to the car. But, if the car’s direction changes and goes the opposite way at the same speed (as with orbit), it is actually then going 77km/s. This is confusing me 😩.

In: Physics

Answer 1

The spacecraft will add its change if velocity over the trajectory if the earth. In the rotation speed this is why most launches are done when possible at lower latitudes and launching east. This way you use earth rotation as a headstart to reach orbital speed.
Regarding earth orbital speed the craft generally just keeps the earth orbital speed as it orbits earth. If the ship escapes earth then it will be orbiting the sun at a speed similar to earth. If you wish to go outwards in solar system (Mars and further) you would need to increase your orbital speed, so you would have to thrust at such place that you escape earth orbit in the general direction of its orbit, therefore at a greater orbital speed.
If on the other hand you want to go to a lower sun orbit you need to decrease orbital speed therefore would accelerate your craft in such way that you escape earth orbit in three opposite direction if it’s orbit around the sun.