Acceleration Due to Gravity of the Earth
The concept of gravitational acceleration is integral in physics, representing how objects are influenced by Earth’s mass. The earth can be conceptualized as a series of concentric spherical shells, which allow us to understand how gravity operates at different distances—both above and below the surface.
Key Points:
- For points located outside the Earth, all mass can be considered to be concentrated at the center, allowing the use of Newton's law of gravitation to determine gravitational force.
- The force experienced by an object inside the Earth varies; shells outside it contribute no force.
- The formula for gravitational force on an object of mass m, at a distance r from the center of the Earth, can be expressed as:
F = (GMm) / r²,
where G is the gravitational constant, M is the mass of the Earth, and r is the distance from the center of the Earth.
- At the surface, the acceleration due to gravity, denoted by g, is determined as:
g = (GM_E) / R_E²,
where R_E is Earth’s radius. The value of g is approximately 9.8 m/s².
- The gravitational force changes with height and depth:
- At height h above the Earth’s surface, the acceleration due to gravity is:
g(h) = g(1 - (h/R_E))
for heights much smaller than the radius of the Earth.
- At depth d below the Earth’s surface, gravitational force is:
g(d) = g(1 - (d/R_E)),
allowing the conclusion that gravitational acceleration decreases as one approaches the center of the Earth.
This section highlights the relationship between gravity and Earth's dimensions, showcasing how gravitational acceleration is a fundamental principle that varies with one's position relative to the center of Earth. It elucidates the nature of gravitational force, encouraging a deeper understanding of universal gravitation concepts.