Astronauts are travelling at 17,500 mph (5mi/sec) when they do space walks outside the ISS

Imagine being the first astronaut jumping out of a space craft untethered and leaving your fate to Newton's First Law of motion (Law of Inertia): It states that an object in motion stays in motion unless acted upon by an external force. When astronauts exit the spacecraft, they already have the same velocity as the spacecraft. In the vacuum of space, with minimal external forces acting on them, they maintain that velocity and continue moving alongside the spacecraft.

When astronauts perform spacewalks outside the International Space Station (ISS), they are able to keep up with the station's speed due to several key principles:

Initial Velocity
When astronauts exit the ISS, they already have the same velocity as the station. This is because they were moving with the ISS while inside, and that motion continues when they exit due to the principle of inertia.

Conservation of Momentum
In the vacuum of space, there is very little to slow down the astronauts once they exit the station. The principle of conservation of momentum means they maintain their velocity unless acted upon by an external force.

Minimal Atmospheric Drag
At the ISS's altitude (about 250 miles above Earth), the atmosphere is extremely thin. The air drag on an astronaut during a spacewalk is negligible, calculated to be around 0.000091 N, which is equivalent to about 0.0003 ounces of force.

Relative Motion
From the perspective of the astronauts and the ISS, there is no relative motion between them. They are all moving together at the same speed relative to Earth.

Tethering
As an additional safety measure, astronauts are typically tethered to the ISS during spacewalks. This ensures they remain connected to the station, even if there were small differences in velocity.

Perception of Speed
Interestingly, despite traveling at about 17,500 mph (28,000 km/h), astronauts don't feel this speed during spacewalks. This is because humans perceive acceleration or force, not constant velocity. In the absence of air resistance or other external forces, there's no sensation of speed.

In summary, astronauts keep up with the ISS during spacewalks primarily because they start with the same velocity as the station and there are minimal forces in the vacuum of space to change that velocity. The principles of inertia and conservation of momentum ensure they continue moving alongside the ISS without any additional effort.