I guess it depends on what you mean by “outer space”. Let’s talk about gravity.
The force of gravity is the attraction that acts between all objects because of their mass. An object’s mass is its amount of matter.
Isaac Newton (the guy who got clunked by the falling apple) wondered how far the force of gravity reached. He used physics to show that the Sun’s force of gravity decreases with distance. Newton deduced that it would work the same for Earth — the farther you’re away from Earth, the weaker the force of gravity. He was right.
He also showed that the object with the most mass has the most gravitational force. The Sun’s mass is greater than Earth’s and its gravitational force is stronger too. (You have gravitational force too, but your mass is so small that it can’t normally be detected.)
So, yes, there is gravity in “outer space” depending on where you are. If you’re close enough to Earth, you’ll be in Earth’s gravitational pull. The Moon is in Earth’s gravitational pull. So is the International Space Station. At 350 kilometers above Earth, it’s being pulled down by Earth’s gravity. The astronauts on-board experience microgravity—they float because they’re literally falling toward Earth.
To blast the Apollo space missions to the Moon, scientists had to use big Saturn V rockets to get the spacecraft out of Earth’s gravitational pull and into the Moon’s gravitational pull. Michael Collins, an astronaut aboard Apollo 11, orbited the Moon 14 times while Buzz Aldrin and Neil Armstrong walked on the Moon. The Moon’s pull is not as strong as Earth’s, and the Apollo command module had enough juice to break free of the Moon and get back home.
Here are a couple of things to think about. First, there is a point between Earth and the Sun, called the Lagrange point, which is a point of equilibrium between Earth’s gravity and the Sun’s. In theory, if you were to go to that point, you would just float there being attracted equally by both the Earth and the Sun.
Finally, if you were to be far enough away from any celestial object, the strength of the gravitational forces would be so small as to be considered non-existent.