Tidal Force on Satellites Calculator

Tidal Force on Satellites Calculator computes tidal force on a satellite, using differential gravity from a celestial body based on distance, size, and masses.

Mass of Celestial Body (kg, e.g., 5.972e24 for Earth):

Distance to Celestial Body (m, e.g., 6.771e6 for LEO):

Satellite Size (Radial Extent, m, e.g., 2):

Satellite Mass (kg, e.g., 1000):

Formulas Used in Tidal Force on Satellites Calculator

The calculator uses the following formulas to estimate tidal forces:

Gravitational Acceleration:

\\[ a(r) = \frac{G M}{r^2} \\]

Tidal Acceleration:

\\[ a_{\text{tidal}} = \frac{2 G M \Delta r}{r^3} \\]

Tidal Force:

\\[ F_{\text{tidal}} = m \cdot a_{\text{tidal}} = m \cdot \frac{2 G M \Delta r}{r^3} \\]

Where:

\\( a(r) \\): Gravitational acceleration (m/s²)
\\( G \\): Gravitational constant (\\( 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \\))
\\( M \\): Mass of celestial body (kg)
\\( r \\): Distance to celestial body (m)
\\( a_{\text{tidal}} \\): Tidal acceleration (m/s²)
\\( \Delta r \\): Satellite size (radial extent, m)
\\( F_{\text{tidal}} \\): Tidal force (N)
\\( m \\): Satellite mass (kg)

Example Calculations

Example 1: LEO Satellite near Earth

Input: Body Mass = \\( 5.972 \times 10^{24} \\) kg, Distance = \\( 6.771 \times 10^6 \\) m, Satellite Size = 2 m, Satellite Mass = 1000 kg

\\[ a(r) = \frac{6.67430 \times 10^{-11} \cdot 5.972 \times 10^{24}}{(6.771 \times 10^6)^2} \approx 8.69 \ \text{m/s}^2 \\] \\[ a_{\text{tidal}} = \frac{2 \cdot 6.67430 \times 10^{-11} \cdot 5.972 \times 10^{24} \cdot 2}{(6.771 \times 10^6)^3} \approx 5.13 \times 10^{-6} \ \text{m/s}^2 \\] \\[ F_{\text{tidal}} = 1000 \cdot 5.13 \times 10^{-6} \approx 0.00513 \ \text{N} \\]

Result: Gravitational Acceleration = 8.69 m/s², Tidal Acceleration = \\( 5.13 \times 10^{-6} \\) m/s², Tidal Force = 0.00513 N

Example 2: Geostationary Satellite near Earth

Input: Body Mass = \\( 5.972 \times 10^{24} \\) kg, Distance = \\( 4.2164 \times 10^7 \\) m, Satellite Size = 5 m, Satellite Mass = 2000 kg

\\[ a(r) = \frac{6.67430 \times 10^{-11} \cdot 5.972 \times 10^{24}}{(4.2164 \times 10^7)^2} \approx 0.224 \ \text{m/s}^2 \\] \\[ a_{\text{tidal}} = \frac{2 \cdot 6.67430 \times 10^{-11} \cdot 5.972 \times 10^{24} \cdot 5}{(4.2164 \times 10^7)^3} \approx 5.33 \times 10^{-8} \ \text{m/s}^2 \\] \\[ F_{\text{tidal}} = 2000 \cdot 5.33 \times 10^{-8} \approx 0.000107 \ \text{N} \\]

Result: Gravitational Acceleration = 0.224 m/s², Tidal Acceleration = \\( 5.33 \times 10^{-8} \\) m/s², Tidal Force = 0.000107 N

Example 3: Satellite near Moon

Input: Body Mass = \\( 7.342 \times 10^{22} \\) kg, Distance = \\( 2.738 \times 10^6 \\) m, Satellite Size = 1 m, Satellite Mass = 500 kg

\\[ a(r) = \frac{6.67430 \times 10^{-11} \cdot 7.342 \times 10^{22}}{(2.738 \times 10^6)^2} \approx 0.653 \ \text{m/s}^2 \\] \\[ a_{\text{tidal}} = \frac{2 \cdot 6.67430 \times 10^{-11} \cdot 7.342 \times 10^{22} \cdot 1}{(2.738 \times 10^6)^3} \approx 4.77 \times 10^{-6} \ \text{m/s}^2 \\] \\[ F_{\text{tidal}} = 500 \cdot 4.77 \times 10^{-6} \approx 0.00239 \ \text{N} \\]

Result: Gravitational Acceleration = 0.653 m/s², Tidal Acceleration = \\( 4.77 \times 10^{-6} \\) m/s², Tidal Force = 0.00239 N

Formulas Used in Tidal Force on Satellites Calculator

Example Calculations

Related To Tidal Force on Satellites Calculator