Variation of Acceleration Due to Gravity Experiment – For Schools, Teachers, and Students
Definition
The acceleration due to gravity (g) varies with altitude and depth relative to the surface of a planet. At a given height above or depth below the surface, the value of g changes based on the distance from the planet’s center and the mass distribution of the planet.
This concept is demonstrated in Dencity – Virtual Lab and Simulations to enhance interactive learning.
Theory
The variation of gravity with altitude (h) and depth (d) can be analyzed as follows:
1. Change in Gravity with Altitude
The acceleration due to gravity at a height h above the surface decreases as the distance from the planet increases. The formula is:
g_h = g (R / (R + h))²
where:
- g_h = Gravity at height h
- g = Gravity at the surface
- R = Radius of the planet
- h = Height above the surface
For small altitudes where h << R, an approximation is:
g_h ≈ g (1 – 2h / R)
2. Change in Gravity with Depth
The acceleration due to gravity decreases linearly with depth inside the planet. The formula is:
g_d = g (1 – d / R)
where:
- g_d = Gravity at depth d
- g = Gravity at the surface
- R = Radius of the planet
- d = Depth below the surface
This linear decrease occurs because only the mass enclosed within the radius (R – d) contributes to the gravitational force, while the outer shell has no net effect (Gauss’s Law for Gravity).
Applications of Gravity Variation
- Calculating gravity variations in satellite orbits and space travel.
- Designing underground experiments or sensitive gravity-based devices.
- Understanding tidal effects and planetary gravity variations.
- Modeling planetary interiors using gravitational measurements.
Real-World Uses
- GPS and Aerospace Engineering: Understanding how altitude affects gravitational acceleration.
- Geophysical Surveys: Detecting density variations within Earth’s crust and mantle.
- Satellite Deployment: Estimating gravitational pull at specific altitudes for orbital calculations.
- Gravity-Based Research: Measuring changes in gravitational acceleration to study the Earth’s crust and core.
- Online Science Lab: Allows students to simulate gravity variations at different altitudes and depths.
Observations and Key Learnings
- Gravity decreases with altitude, following the 1/r² relationship.
- Gravity decreases linearly with depth until reaching the core (assuming uniform density).
- At extreme altitudes or depths, gravitational variations impact orbital mechanics and geophysical studies.
- The simplified formulas for g_h and g_d help in making quick approximations for small height or depth changes.
This Variation of Acceleration Due to Gravity experiment helps students understand how gravity changes with altitude and depth. By exploring gravitational variations, learners can analyze real-world applications in satellite motion, planetary interiors, and geophysics.
With our science education app, students can learn physics online through science practical simulators. Our virtual lab provides interactive simulations that allow users to explore how gravitational acceleration is affected by height and depth, making complex physics concepts more engaging and practical.
