What is Tidal Force?

Description

The tidal force is the secondary effect of the gravitational force, which is responsible for the phenomenon of tides. It arises because the gravitational field exerted by a celestial body (like the Moon) is not uniform across the diameter of another body (like the Earth). The side of the Earth closer to the Moon experiences a stronger pull than the center, and the far side experiences a weaker pull. This difference in gravitational force creates a stretching effect, or tidal bulge, on both sides of the Earth.

This force is crucial in astrophysics, governing everything from Earth-Moon ocean tides and the synchronization of planetary rotation to the potential destruction of objects orbiting black holes (spaghettification) or the Roche limit of planetary ring systems. This calculator determines the maximum differential force $F_t$ experienced by an object of radius $R$ due to a massive body $M$.

How to Use the Calculator

1. Mass of Celestial Body ($M$): Enter the mass of the large gravitational body (e.g., the Moon or a star) in kilograms (kg). Use scientific notation (e.g., $5.97\text{e}24$).
2. Mass of Object ($m$): Enter the mass of the smaller object experiencing the force in kilograms (kg).
3. Radius of Object ($R$): Enter the radius of the object ($m$) in meters (m). This is half the distance over which the differential force acts.
4. Distance Between Centers ($d$): Enter the distance separating the center of the celestial body ($M$) and the center of the object ($m$) in meters (m).
5. Click the “Calculate Tidal Force” button to see the step-by-step substitution and the final result $F_t$ in Newtons (N).