“That there is no gravity in space”. People do not have a good understanding of what weightlessness is. They see astronauts floating around inside and outside a spacecraft and reach the conclusion that there is no gravity.
Anywhere mass and space exist, gravity exists. Gravity is the curvature of spacetime due to the presence of mass. The gravitational influence from the Sun that keeps the Earth in orbit around the Sun is felt equally by the astronauts in space. The gravitational influence from the Earth that keeps the Moon and the ISS in Earth orbit is also felt by the astronauts floating inside and outside the spacecraft. If these influences were not felt, the astronauts would not stay in orbit.
At the altitude the astronauts in the International Space Station (ISS) inhabit, the gravitational influence from the Earth is 8.75 m/s^2. That is only about 11% less than the 9.81 m/s^2 felt by you and me, on the Earth’s surface.
They are weightless and appear to float because they are in freefall. A spacecraft in Earth orbit is falling towards the Earth (because of gravity) but also moving forward at a speed high enough that the path traveled isn’t straight down, but instead a curve that circles the Earth. The astronaut is falling and so is their spacecraft. If both are falling, there is no force of one against the other and thus no sensation of weight. We can emulate this freefall here on Earth, in a tall chamber that is pumped to vacuum.
Let’s do a thought experiment.
Imagine an astronaut on Earth standing on a scale. The scale would indicate weight because gravity is pulling the astronaut towards the center of the Earth but the Earth isn’t willing to get out of the way. Weight is the perception of the Earth not getting out of the way.
Now imagine that same astronaut in space, orbiting the Earth. He has the same scale, and he stands upon it. Will it show weight? No. It won’t show weight because the astronaut and scale are falling together and there is no contact with the Earth to allow the Earth to push back.
The ISS and its crew are in free fall. They are falling towards the center of the Earth but since they are also moving quickly, sideways, they keep missing the Earth. Since there is no Earth surface to push back against the ISS or its crew, there is weightlessness.
Source: Quora, Answered by Mr. Robert Frost, Instructor and Flight Controller at NASA