When we talk about work done by gravity, we need to understand how work is calculated. Work is done when a force causes an object to move. The amount of work done can be calculated using the formula: \[ W = F \cdot d \cdot \cos(\theta) \] Here,
- \( W \) is the work done,
- \( F \) is the force applied,
- \( d \) is the displacement of the object, and
- \( \theta \) is the angle between the force and the displacement vectors.
In the context of the International Space Station, gravity acts as a centripetal force that keeps it in orbit. Importantly, this force is always directed toward the center of the Earth and is perpendicular to the path (displacement) of the space station in a circular orbit. When the angle \( \theta \) is 90 degrees, as it is in this circular motion, \( \cos(90^\circ) = 0 \). Consequently, the work done by gravity is zero because the displacement is perpendicular to the force of gravity.
This is a key feature in any circular orbit where gravity acts as a centripetal force: no energy is added or taken away by gravity, maintaining constant motion.