The gravitational force acting on a mass is directly proportional to the product of the masses and inversely proportional to the square of the distance between the masses. This is why it is easy to see that a 70-kg physics student weighs less on an airplane at 40000 feet above the Earth’s surface than on the ground.
In the real world, however, spacecraft and astronauts do not experience a weightless environment. This is because orbiting spacecraft are moving so fast that the acceleration of their path matches the curve of Earth’s gravity, which keeps them in orbit.
It is important to understand this concept because students often get confused when learning about the relationship between the g-force experienced during acceleration and weightlessness. They might confuse this force with the one that produces weight on an object, which is the result of a reaction to the force of gravity and is equal and opposite to it.
This is a very dangerous mistake because it means that the g-force experienced by a rocket as it accelerates counter-clockwise on its orbital trajectory is exactly the same as the g-force it would feel on the Earth’s surface as it falls back down to it (a negative g-force producing downward weight).
It is also worth noting that there are special points in two-body gravitational systems called Lagrange points that are very close to the center of mass and that we sometimes send things there. If a spaceship is in an elliptical orbit that passes very closely by the Earth, it will have to remain at the L1 Lagrange point in order to retain its orbital speed and stay within the gravitational pull of the Earth.
