Yes, gravitational acceleration definitively depends on distance. Gravitational acceleration decreases as the distance from the center of a massive object increases.
Explanation of Gravitational Acceleration and Distance
Gravitational acceleration is the acceleration experienced by an object due to the force of gravity. Newton's Law of Universal Gravitation and its subsequent derivation of gravitational acceleration demonstrate this relationship clearly. The equation for gravitational acceleration (g) is:
g = GM/r²
Where:
- G is the gravitational constant (approximately 6.674 × 10⁻¹¹ N⋅m²/kg²)
- M is the mass of the object creating the gravitational field (e.g., a planet)
- r is the distance from the center of the massive object to the point where you're measuring the acceleration.
From the equation, it's evident that gravitational acceleration (g) is inversely proportional to the square of the distance (r). This means that as the distance (r) increases, the gravitational acceleration (g) decreases, and vice versa. If you double the distance, the gravitational acceleration becomes one-quarter of what it was. If you triple the distance, the gravitational acceleration becomes one-ninth of what it was, and so on.
Example
Consider an object on the surface of Earth. The gravitational acceleration is approximately 9.8 m/s². If you were to move that object to a distance equal to the Earth's radius above the surface (effectively doubling the distance from the Earth's center), the gravitational acceleration would decrease to approximately 2.45 m/s² (9.8 / 4 = 2.45).
In Summary
Gravitational acceleration weakens significantly with increasing distance from the source of the gravitational field. The relationship is an inverse square law.
