[winodog]

Me too. I also wonder “if the sun is moving through space at 500 Kms a second then how would a spaceship keep up once it left the gravity of well?”

[winodog]

Gravity well of earth.

[Yo-Yo]

I also wonder “if the sun is moving through space at 500 Kms a second then how would a spaceship keep up once it left the gravity [well of Earth]?”

Because it was given that same 500 Km/S speed just by being built on Earth. It's not like a cigarette butt thrown out the window of a speeding car. There is no air resistance to slow it down.

[KarlInOhio]

Intertia. It's moving at the same speed as the sun (with the additional speed of Earth's motion around the sun and Earth's rotational speed at launch). Imagine tossing a ball out your car window when driving 65 mph, except there is no air resistance to slow it or gravity to pull it down. It would keep going 65 mph next to you, drifting sideways from you at the speed you threw it.

When the Apollo missions left Earth, they were in orbit around the sun in almost exactly the same direction and speed as the Earth.