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?

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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 😩.

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You’re not confused. The spacecraft’s velocity *relative to Earth* changes as the earth revolves around the sun while the spacecraft continues in a straight line.

You have the general idea correct, it is beneficial to launch the probe in the direction of both the rotation and orbit of Earth to use that existing velocity. Keep in mind though that there is no absolute frame of reference for the probe’s “true velocity”.

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.

Orbital direction definitely matters.

You’ll notice most rockets are launched as close to the equator as their country can and generally launched towards the East, this gives them a bit of a speed boost to help get into orbit but not much. Getting into orbit requires a speed of 8000 m/s but launching from the equator instead of the pole only saves you about 400 m/s.

To go from Earth orbit to a further out planet like Mars or Jupiter you need to add more energy to your spacecraft. Since your orbit is now referenced to the sun then burning the engine in the same direction of Earth’s orbit gives you a 40 km/s head start. If you tried to get to Mars by burning the opposite direction you first need to slow down 40 km/s, then speed back up by 40 km/s, ***then*** add the energy to get you out to Mars’s orbit. We don’t have a rocket that can do that so we always go the same direction as Earth

> 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.

Right. If you jump off the front of the car, then the car is hurtling toward you, so the gap between you and the car is smaller than it would be if the car were parked. If you jump off the back of the car, the car is hurtling away from you, so the gap between you and the car is larger than it would be if the car were parked. Since speed is distance divided by time and the *moving* car is your zero-point, your speed from the perspective of the car (that is, from the perspective that the car is actually perfectly still and it’s **the universe** that’s hurtling past at 30 km/s) will be faster when you jump off the rear of the car than when you jump off the front.

Pretty much all spacecraft intended to go into a roughly equatorial orbit launch from West to east to take advantage of the 1500 kmh boost from the Earth’s rotation. The only exception I can think of is Israel, which launches the other way so they can dump their rocket stages in the Mediterranean instead of on the countries east of them.

The interplanetary component is somewhat hard to explain so I recommend trying out games like Kerbal Space Program for PC and console or Spaceflight simulator for your phone. The physics in the two are mostly realistic and trying is the best way of learning.

In short, all the planets’s speed relative to the sun has to be taken into account when performing deep space transfers because it is so significant. Since every planet orbits the same direction, this is made simpler and easier because that reduces the relative speeds between them.

You’ve kind of got it. For a near-equatorial satellite, there is a huge advantage to launching near the equator and towards sunrise.

Like the car, the path of the satellite is completely independent of the Earth’s rotation after launch. Unlike the car, both the orbit and the rotation are periodic (repeating) functions. This means that you can pick orbits that have certain relationships to the Earth’s surface. For example at an orbital height of about 36,000 km, the orbital period is about 24 hours. A satellite placed at that height over the equator will seem to be stationary from the perspective of the Earth’s surface. This is a geostationary or geosynchronous orbit. In the case of polar orbits (that go around the earth from top to bottom) the Earth rotates under the satellite. If the orbit is tilted just very slightly so that the orbital plane precesses around the earth once per year, the satellite will always pass overhead at the same times of the solar day (eg: sunrise and sunset). This is called a “sun synchronous orbit” and is really useful for many studies involving imagine.