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Surface Gravity Formula:
where \( r = \left(\frac{3M}{4\pi\rho}\right)^{1/3} \)
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Surface gravity (g) is the gravitational acceleration experienced at the surface of a celestial body. It depends on the body's mass and radius, and can be calculated from density when radius is not directly known.
The calculator uses the surface gravity formula:
where \( r = \left(\frac{3M}{4\pi\rho}\right)^{1/3} \)
Where:
Explanation: The formula calculates gravitational acceleration at the surface by combining Newton's law of universal gravitation with the relationship between mass, density, and radius.
Details: Surface gravity calculations are essential in astrophysics, planetary science, and space exploration for understanding celestial body characteristics, orbital mechanics, and potential habitability.
Tips: Enter mass in kilograms and density in kilograms per cubic meter. Both values must be positive numbers. The calculator will compute the radius from density and then calculate surface gravity.
Q1: What is the gravitational constant (G)?
A: G is the fundamental physical constant that measures the strength of the gravitational force between two bodies. Its value is approximately 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻².
Q2: How is radius calculated from density?
A: For a spherical body, radius is derived from the formula \( r = \left(\frac{3M}{4\pi\rho}\right)^{1/3} \), which comes from the relationship between mass, volume, and density.
Q3: What are typical surface gravity values?
A: Earth: ~9.8 m/s², Moon: ~1.6 m/s², Mars: ~3.7 m/s², Jupiter: ~24.8 m/s². Values vary significantly across different celestial bodies.
Q4: Does this calculation assume a spherical body?
A: Yes, the calculation assumes the celestial body is perfectly spherical and has uniform density throughout.
Q5: Can this be used for non-spherical bodies?
A: For irregular shapes, the calculation provides an approximation. More complex modeling is needed for precise gravity field calculations of non-spherical bodies.