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Calcimator

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
  1. Enter Primary Mass (solar masses) — the dominant gravitational body, such as a star.
  2. Enter Secondary Mass (solar masses) and Secondary Radius (solar radii) — the smaller orbiting body.
  3. Set Orbital Distance (AU) between the two bodies — reducing this dramatically increases tidal acceleration.
  4. Read Tidal Acceleration (m/s²) and Tidal Force (N) acting across the secondary's diameter.
  5. 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 MassTidal AccelerationTidal ForceRoche Limit
1000.000000232 m/s²1,382,620,696,166,903,000 N0 AU
3500.000000811 m/s²4,839,172,436,584,160,000 N0 AU
6500.000001506 m/s²8,987,034,525,084,869,000 N0 AU
9000.000002085 m/s²12,443,586,265,502,126,000 N0 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) / d³

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Primary Mass = 1, Secondary Mass = 0.000003, Orbital Distance = 1, Secondary Radius = 0.000042 = 4 input(s) provided
  2. Calculate Tidal Acceleration
    Tidal Acceleration
    2e-9 = 2e-9
  3. Calculate Tidal Force
    Tidal Force
    13826206961669026 = 13826206961669026
  4. Calculate Roche Limit
    Roche Limit
    0 = 0
  5. Calculate Hill Sphere Radius
    Hill Sphere Radius
    0.01 = 0.01
  6. Calculate Tidal Locking Timescale
    Tidal Locking Timescale
    5.683538469477855e+37 = 5.683538469477855e+37

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