Tidal Force Calculator

About the Tidal Force Calculator

The Tidal Force Calculator computes the differential gravitational force exerted by a massive body on another body, causing tidal effects. This tool is designed for astronomers, astrophysicists, and students studying celestial mechanics.

Tidal Force: The gravitational force difference across a body due to a nearby massive object, responsible for phenomena like ocean tides, tidal heating, and Roche limit disruptions.

Use this calculator to determine the tidal force for a given system of celestial bodies.

• Features:
  • Calculates tidal force (\( F_t \)).
  • Inputs include masses (\( M \), \( m \)), radius (\( r \)), and distance (\( d \)).
  • Keypad includes digits (0–9) and decimal point (.).
  • Displays step-by-step calculations in LaTeX format.
  • Clear and backspace functionality, with a "Copy" button for results.
  • Uses MathJax for professional rendering of mathematical expressions.
• Practical Applications: Useful in studying tidal interactions, satellite stability, and planetary geology.
• How to Use:
  • Enter mass of the massive body (\( M \), in Solar masses).
  • Enter mass of the affected body (\( m \), in Earth masses).
  • Enter radius of the affected body (\( r \), in kilometers).
  • Enter distance between centers (\( d \), in AU).
  • Use the keypad to input digits and decimal points.
  • Click "Calculate" to compute the tidal force.
  • Use "Clear" to reset or "⌫" to delete the last character.
  • Use "Copy" to copy the results and steps.
  • Share or embed the calculator using the action buttons.
• Helpful Tips:
  • All inputs must be positive numbers.
  • Typical values: \( M \) (0.1–2 Solar masses), \( m \) (0.001–100 Earth masses), \( r \) (1000–10000 km), \( d \) (0.001–100 AU).
  • Earth mass ≈ 5.972 × 10²⁴ kg, Solar mass ≈ 1.989 × 10³⁰ kg, 1 AU ≈ 1.496 × 10⁸ km.
  • The formula assumes point masses; for extended bodies, results are approximate.
  • Ensure \( d \) is greater than the sum of the bodies' radii to avoid overlap.
• Examples:
  • Example 1: Moon's tidal force on Earth:
    • Inputs: \( M = 0.0000123 \) Solar masses (Moon), \( m = 1.0 \) Earth mass, \( r = 6371 \) km, \( d = 0.00257 \) AU
    • Steps:
      • Convert units: \( M = 7.342 × 10^{22} \) kg, \( m = 5.972 × 10^{24} \) kg, \( d = 3.844 × 10^5 \) km
      • Numerator: \( 2 G M m r \)
      • Denominator: \( d^3 \)
      • Tidal force: \( F_t = \\frac{2 G M m r}{d^3} \)
    • Result: \( F_t \approx 1.1 × 10^{17} \) N
  • Example 2: Sun's tidal force on Earth:
    • Inputs: \( M = 1.0 \) Solar mass, \( m = 1.0 \) Earth mass, \( r = 6371 \) km, \( d = 1.0 \) AU
    • Steps: Similar calculations.
    • Result: Computed tidal force.

Analyze tidal effects with this interactive calculator. Share or embed it on your site!