If two objects are tidally locked to each other, a. the tides always stay on the same place on each object. b. the objects always remain in the same place in each other's sky. c. the objects are falling together. d. both a and b

The rotational period of an object is the time it takes for the object to complete one full rotation on its axis.
For example, Earth’s rotational period is 24 hours, meaning it takes 24 hours for our planet to spin once around its axis.
In the context of tidal locking, the rotational period is crucial. When an object is tidally locked, its rotational period syncs up with its orbital period.
This means it takes the same amount of time to rotate once around its axis as it does to orbit around the object it is locked to.
This synchronization ensures that the same face of the tidally locked object always faces the object it is orbiting.
This phenomenon is why we always see the same side of the Moon from Earth.
Tidal locking is a result of gravitational forces and can take millions to billions of years to occur, depending on the masses and distances involved.

The orbital period refers to the time it takes for an object to complete one full orbit around another object.
In our Solar System, different planets have different orbital periods based on their distance from the Sun.
For example, Earth’s orbital period is 365.25 days, which we call a year.
When objects are tidally locked, their orbital periods are equal to their rotational periods.
This means the time it takes for them to orbit around each other is the same as the time it takes for them to complete one spin.
This synchronicity causes the same sides of the objects to always face each other, leading to a consistent view of one object from the other.
For instance, the Moon’s orbital period around Earth is about 27.3 days, which matches its rotational period, resulting in tidal locking.

Gravitational interaction is the force that attracts two bodies towards each other.
This is the fundamental force that causes planetary and satellite orbits.
Gravitational forces depend on two main factors: the masses of the objects and the distance between them.
The bigger the masses and the shorter the distance, the stronger the gravitational pull.
In tidal locking, gravitational interaction is responsible for altering the rotational periods of the involved objects until they match their orbital periods.
Imagine a planet and its moon exerting tidal forces on each other.
These forces create bulges on their surfaces, deforming them slightly.
Over long periods, these tidal bulges act like brakes on each object's rotation, eventually leading to tidal locking.
Thus, gravitational interaction is not just about keeping objects in orbit but also about synchronizing their rotations and orbits over time.