The key difference between small 'g' and capital 'G' in physics is that G is the universal gravitational constant, while g is the acceleration due to gravity.
Understanding Gravitational Constant (G)
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Definition: Capital G (G) represents the universal gravitational constant. It's a fundamental constant that describes the strength of the gravitational force between any two objects with mass.
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Value: The value of G is approximately 6.674 x 10-11 Nm2/kg2. This value is the same everywhere in the universe.
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Role in the Universal Law of Gravitation: G is a key component in Newton's Law of Universal Gravitation, which states that the gravitational force (F) between two objects with masses m1 and m2, separated by a distance r, is:
F = G (m1 m2) / r2
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It is a constant: The value of G remains constant regardless of the mass or distance between the objects.
Understanding Acceleration Due to Gravity (g)
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Definition: Small g (g) represents the acceleration due to gravity experienced by objects near the surface of a celestial body, like Earth. It is the acceleration at which objects fall freely when the only force acting on them is gravity.
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Value (on Earth): The approximate value of g on Earth is 9.8 m/s2. This means that the velocity of a falling object increases by 9.8 meters per second every second.
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Not a Universal Constant: Unlike G, the value of g is not constant and varies depending on:
- Location on Earth: g is slightly different at different locations due to the Earth's shape (it's not a perfect sphere) and variations in density.
- Altitude: g decreases as you move further away from the Earth's surface (increase in altitude).
- Other Celestial Bodies: g is different on other planets or moons due to their different masses and radii.
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Relationship to G: The acceleration due to gravity (g) is related to the universal gravitational constant (G), the mass of the celestial body (M), and the radius of the celestial body (R) by the following equation:
g = G * M / R2
Key Differences Summarized
| Feature | Universal Gravitational Constant (G) | Acceleration Due to Gravity (g) |
|---|---|---|
| Definition | Universal constant of gravitation | Acceleration due to gravity |
| Value | 6.674 x 10-11 Nm2/kg2 | Approximately 9.8 m/s2 (on Earth) |
| Constant? | Yes | No |
| Dependence | Independent of location/body | Dependent on location/body |
| Role | Determines the strength of gravity | Acceleration of falling objects |
In summary, G is a fundamental constant defining the strength of gravity, while g is the acceleration experienced by objects due to gravity on a specific celestial body, like Earth, and its value varies.
