Tidal Force Calculator
Calculate tidal forces, Roche limit, Hill sphere, and tidal locking timescales for celestial bodies.
Inputs
Solar Masses
Solar Masses
AU
Solar Radii
Results
Tidal Acceleration
0.000000002 m/s²
Tidal Force
13,826,206,961,669,026 N
Roche Limit
0 AU
Hill Sphere Radius0.01 AU
Tidal Locking Timescale56,835,384,694,778,550,000,000,000,000,000,000,000 million years
How to Use This Calculator
- Enter Primary Mass (solar masses) — the dominant gravitational body, such as a star.
- Enter Secondary Mass (solar masses) and Secondary Radius (solar radii) — the smaller orbiting body.
- Set Orbital Distance (AU) between the two bodies — reducing this dramatically increases tidal acceleration.
- Read Tidal Acceleration (m/s²) and Tidal Force (N) acting across the secondary's diameter.
- Use Roche Limit (AU), Hill Sphere Radius (AU), and Tidal Locking Timescale (million years) to characterize the system's dynamical state.
How the result changes with Primary Mass
| Primary Mass | Tidal Acceleration | Tidal Force | Roche Limit |
|---|---|---|---|
| 100 | 0.000000232 m/s² | 1,382,620,696,166,903,000 N | 0 AU |
| 350 | 0.000000811 m/s² | 4,839,172,436,584,160,000 N | 0 AU |
| 650 | 0.000001506 m/s² | 8,987,034,525,084,869,000 N | 0 AU |
| 900 | 0.000002085 m/s² | 12,443,586,265,502,126,000 N | 0 AU |
What each input means
- Primary Mass
- Mass of primary body (e.g., star)
- Secondary Mass
- Mass of secondary body (e.g., planet)
- Orbital Distance
- Distance between bodies
- Secondary Radius
- Radius of secondary body
How this is calculated
Formula
a_tidal = (2GM × r) / d³Worked example, using the default values
- Identify Input Parameters4 parametersPrimary Mass = 1, Secondary Mass = 0.000003, Orbital Distance = 1, Secondary Radius = 0.000042 = 4 input(s) provided
- Calculate Tidal AccelerationTidal Acceleration2e-9 = 2e-9
- Calculate Tidal ForceTidal Force13826206961669026 = 13826206961669026
- Calculate Roche LimitRoche Limit0 = 0
- Calculate Hill Sphere RadiusHill Sphere Radius0.01 = 0.01
- Calculate Tidal Locking TimescaleTidal Locking Timescale5.683538469477855e+37 = 5.683538469477855e+37
Related Calculators
The questions that sit next to this one — chosen by subject, including calculators filed under a different category.
Astrophysics & Astronomy
Roche Limit Calculator
Calculate Roche limit - the minimum distance a satellite can orbit before being torn apart by tidal forces.
Astrophysics & AstronomyOrbital Period Calculator
Calculate orbital period using Kepler's laws. Find orbital velocity, angular velocity, and perihelion/aphelion distances.
Geometry & MeasurementSphere Calculator
Calculate the volume and surface area of a sphere from its radius.
Astrophysics & AstronomyEscape Velocity Calculator
Calculate escape velocity, orbital velocity, and gravitational parameters for celestial bodies.
More in Science & Physics.