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When we talk about an astronaut's weight, we're referring to the force exerted by gravity on their mass. On Earth, this force is straightforward: it's simply their mass multiplied by the acceleration due to Earth's gravity, or

• Weight = mass × gravity (which is about 9.81 m/s²).

However, when an astronaut is in space, especially at a height of 600 km above the Earth's surface while repairing something like the Hubble Space Telescope, calculating this becomes a bit more complex.

At this altitude, the force of gravity is still there but is weaker than on the ground.
The astronaut's "weight" as felt by them isn't the same as it would be on Earth.
This might seem counterintuitive since we often assume they are weightless in space, but we'll get into why this is the case later.

Earth's gravity is the force that keeps everything anchored to our planet. It pulls objects towards the Earth's center. The strength of this force diminishes with distance from the Earth's surface.

• Near the surface, gravity is strong enough to keep everything, from people to oceans, firmly in place.

When you are still relatively close to Earth, like a few hundred kilometers up, gravity still has a strong hold.
The gravitational force can be calculated using the equation: \[ F = \frac{G M m}{R^2} \]where

• \( G \) is the universal gravitational constant, approximately \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \),
• \( M \) is Earth's mass,
• \( m \) is the object's mass, and
• \( R \) is the distance from the center of the Earth.

Therefore, even at 600 km above the Earth's surface, an astronaut is still under the influence of gravity, albeit slightly less than at ground level.

Orbital mechanics are the rules governing movements of objects in space under the influence of gravitational forces. When an astronaut is orbiting Earth, they are subject to these principles. Imagine throwing a ball so fast that rather than falling back to the ground, it keeps missing the Earth, following a curved path around it.

• This is essentially what happens in orbit – the astronaut is in constant free fall towards Earth, but their forward motion keeps them in a continuous path around the planet.

In this state, the astronaut and their spacecraft are moving at such speeds that their downward motion due to gravity is perfectly matched by their forward motion.

This combination keeps them floating along a stable path, like dancing with destiny, around the Earth.

Despite gravity still acting on astronauts, they experience a sensation of weightlessness. This isn't because the gravitational force is negligible. Instead, it's due to their condition of "free fall", which is the same state achieved when skydiving briefly before a parachute deploys.

• As both the astronaut and their ship are falling, everything inside moves at the same rate, effectively "floating" relative to one another.

This is why astronauts appear to be weightless while working in space despite Earth's gravity still pulling on them. They are in a state of continuous free fall, causing them to feel as though they carry no weight at all.

Weightlessness thus is more accurately a term for the synchronized free-fall of an astronaut and their environment, rather than an absence of gravitational force.