Here is the solar system. The planets are the people in the swings, the sun is the center of the ride. The gravitational force from the sun are the cables supporting the riders.

Even though our speed circling the solar system is preventing our planet from falling into the sun, from the perspective of the planet, it doesn't feel like we're just leisurely floating. It feels a little more like this

Just like on any spinny ride, if you find a way off of it while it's still going, it gives you a little boost away from itself

Comparatively, the energy required to fly off the ride

is nearly passive next to the energy required to claw your way to the center