Gravitational Wave Signal Strength Calculator

Gravitational Wave Signal Strength Calculator computes strain amplitude from a binary system, using masses, distance, and frequency for astrophysical analysis.

Mass of First Object (kg):

Mass of Second Object (kg):

Distance to Source (m):

Gravitational Wave Frequency (Hz):

Formulas Used in Gravitational Wave Signal Strength Calculator

The calculator uses the following formulas to estimate gravitational wave strain:

Reduced Mass:

\\[ \mu = \frac{m_1 m_2}{m_1 + m_2} \\]

Strain Amplitude:

\\[ h = \frac{4 (G \mu)^{5/3}}{c^4 r} (\pi f)^{2/3} \\]

Where:

\\( \mu \\): Reduced mass (kg)
\\( m_1, m_2 \\): Masses of the two objects (kg)
\\( G \\): Gravitational constant (\\( 6.67430 \times 10^{-11} \, \text{m}^3 \text{kg}^{-1} \text{s}^{-2} \\))
\\( c \\): Speed of light (\\( 2.99792458 \times 10^8 \, \text{m/s} \\))
\\( r \\): Distance to source (m)
\\( f \\): Gravitational wave frequency (Hz)
\\( h \\): Strain amplitude (dimensionless)

Example Calculations

Example 1: Binary Neutron Star Merger

Input: \\( m_1 = 2.7816 \times 10^{30} \\) kg (1.4 \\( M_\odot \\)), \\( m_2 = 2.7816 \times 10^{30} \\) kg, Distance = \\( 1.234272 \times 10^{25} \\) m (400 Mpc), Frequency = 100 Hz

\\[ \mu = \frac{2.7816 \times 10^{30} \cdot 2.7816 \times 10^{30}}{2.7816 \times 10^{30} + 2.7816 \times 10^{30}} \approx 1.3908 \times 10^{30} \ \text{kg} \\] \\[ h = \frac{4 (6.67430 \times 10^{-11} \cdot 1.3908 \times 10^{30})^{5/3}}{(2.99792458 \times 10^8)^4 \cdot 1.234272 \times 10^{25}} (\pi \cdot 100)^{2/3} \approx 2.18 \times 10^{-21} \\]

Result: Reduced Mass = \\( 1.3908 \times 10^{30} \\) kg, Strain Amplitude = \\( 2.18 \times 10^{-21} \\)

Example 2: Binary Black Hole Merger

Input: \\( m_1 = 5.967 \times 10^{31} \\) kg (30 \\( M_\odot \\)), \\( m_2 = 5.967 \times 10^{31} \\) kg, Distance = \\( 3.08568 \times 10^{25} \\) m (1 Gpc), Frequency = 50 Hz

\\[ \mu = \frac{5.967 \times 10^{31} \cdot 5.967 \times 10^{31}}{5.967 \times 10^{31} + 5.967 \times 10^{31}} \approx 2.9835 \times 10^{31} \ \text{kg} \\] \\[ h = \frac{4 (6.67430 \times 10^{-11} \cdot 2.9835 \times 10^{31})^{5/3}}{(2.99792458 \times 10^8)^4 \cdot 3.08568 \times 10^{25}} (\pi \cdot 50)^{2/3} \approx 3.51 \times 10^{-21} \\]

Result: Reduced Mass = \\( 2.9835 \times 10^{31} \\) kg, Strain Amplitude = \\( 3.51 \times 10^{-21} \\)

Example 3: Asymmetric Binary System

Input: \\( m_1 = 1.989 \times 10^{31} \\) kg (10 \\( M_\odot \\)), \\( m_2 = 9.945 \times 10^{31} \\) kg (50 \\( M_\odot \\)), Distance = \\( 1.54284 \times 10^{25} \\) m (500 Mpc), Frequency = 80 Hz

\\[ \mu = \frac{1.989 \times 10^{31} \cdot 9.945 \times 10^{31}}{1.989 \times 10^{31} + 9.945 \times 10^{31}} \approx 1.6575 \times 10^{31} \ \text{kg} \\] \\[ h = \frac{4 (6.67430 \times 10^{-11} \cdot 1.6575 \times 10^{31})^{5/3}}{(2.99792458 \times 10^8)^4 \cdot 1.54284 \times 10^{25}} (\pi \cdot 80)^{2/3} \approx 4.02 \times 10^{-21} \\]

Result: Reduced Mass = \\( 1.6575 \times 10^{31} \\) kg, Strain Amplitude = \\( 4.02 \times 10^{-21} \\)

Formulas Used in Gravitational Wave Signal Strength Calculator

Example Calculations

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