Acceleration due to gravity, variation with altitude and depth

The acceleration due to gravity (g) is the acceleration experienced by an object due to the gravitational pull of the Earth.
The standard value of g at the Earth's surface is approximately 9.8 m/s².
g is calculated using the formula g = GM/R², where G is the gravitational constant, M is the Earth's mass, and R is its radius.
The value of g is maximum at the Earth’s surface and decreases with altitude, depth, and latitude.
At higher altitudes, g decreases because the distance (r) from the Earth’s center increases.
The formula for g at an altitude h is g' = g(1 - 2h/R) for small heights h, where R is the Earth’s radius.
For greater heights, g is calculated as g' = GM / (R + h)².
At a very large distance from the Earth, g approaches zero.
Variation of g with depth is linear, decreasing as we move toward the Earth’s center.
The formula for g at depth d is g' = g(1 - d/R), where d is the depth and R is the Earth’s radius.
At the Earth’s center, g is zero because gravitational forces cancel out due to symmetry.
The decrease in g with altitude is more significant for larger heights, following the inverse-square law.
The decrease in g with depth is proportional to the distance from the Earth’s center.
g also varies with latitude due to the Earth’s rotation and its oblate spheroid shape.
The effective value of g is slightly higher at the poles and lower at the equator.
The increase of g at the poles is due to the shorter radius of the Earth at the poles.
The decrease of g at the equator is due to the centrifugal force arising from the Earth’s rotation.
At a given latitude, the value of g decreases with altitude, following the formula g' = g - 2h/R for small altitudes.
The variation of g affects the weight of an object, as weight is given by W = mg.
Objects weigh slightly less at the equator compared to the poles.
Changes in g due to depth are crucial for understanding phenomena in geophysics and mining.
The concept of varying g is used in designing satellites and space missions.
The decrease in g with altitude influences the orbital velocity of satellites.
For objects moving inside the Earth (e.g., tunnels), g decreases as they approach the Earth’s core.
The variation of g is negligible for small altitudes, making it nearly constant in everyday applications.
The study of g’s variation helps in measuring the Earth’s density and structure.
g is affected by local geological features, such as mountains and mineral deposits.
The phenomenon of microgravity occurs in orbiting spacecraft where g is effectively zero.
The value of g plays a crucial role in determining the escape velocity of a planet.
Escape velocity is given by vₑ = √(2gR), where R is the radius of the planet.
The study of g’s variation is critical in understanding the motion of projectiles at high altitudes.
g’s variation with depth is used to calculate the gravitational pull at different layers of the Earth.
The concept of g is essential in analyzing the behavior of pendulums at different locations.
Satellites in low Earth orbit experience a slightly lower value of g, affecting their orbital period.
The reduction of g with altitude is vital in designing efficient space launch systems.
g is a key parameter in studying free-fall motion near the Earth’s surface.
Variations in g affect the calculation of potential energy, which is given by U = mgh.
The study of g is crucial for understanding the Earth’s gravitational anomalies.
g’s dependency on altitude is used to calculate the height of geostationary orbits.
For high-altitude systems, changes in g influence aerodynamic forces and flight dynamics.
The variation of g with depth is significant in analyzing the Earth’s interior using seismic waves.
In space missions, changes in g are accounted for to ensure the proper functioning of equipment.
g’s variation with altitude and depth is a fundamental topic in gravitational studies and astrophysics.
At the Earth’s surface, small variations in g are used to locate underground oil and minerals.