Earth's Gravity

Studies Earth's gravitational acceleration and its variation with altitude, latitude, depth, and mass distribution.

Conceptual context

Earth's gravity does not have exactly the same value everywhere. It changes with $h$, $\phi$, planetary shape, and internal mass distribution. Near the surface it is often approximated by an almost constant $g_0$, but that simplification is insufficient for mountains, satellites, geodetic studies, or interior models. $g$ describes local field strength, whereas $P$ also depends on $m$. Separating these quantities clarifies what belongs to Earth, what belongs to the object, and what comes from the selected model.

🟢 Essential level

Earth's $g$ decreases as $h$ increases because the observation point moves farther from the center and the field spreads over larger surfaces.

It also changes with $\phi$. Near the equator, Earth's rotation slightly reduces effective gravity and the planetary radius is larger; toward the poles, both effects make gravity somewhat stronger. $g_0$ is therefore a reference, not an identical universal value. $m$ does not change when an object moves, but its $P$ changes because local gravity changes. Inside an ideal uniform Earth, gravity decreases with $d$ and vanishes at the center by symmetry. Every problem must distinguish surface, exterior, latitude, and interior before calculation. This distinction identifies the physical cause, the correct distance, and the valid approximation before any substitution, and skipping it is the most common source of sign errors and wrongly scaled results in this topic, especially when altitude and depth are casually treated as interchangeable quantities rather than distinct physical variables.

🔵 Formal level

Basic formulas

For a spherical Earth, surface gravity depends on $G$, $M_T$, and $R_T$:

Gravity at a spherical surface

At exterior $h$, distance from the center is $R_T$ plus $h$, so use:

Gravity with altitude

These two expressions describe the same exterior gravitational field, applied first at the surface and then at a larger radial distance.

Real student questions

Why use 9.81 m/s² if gravity changes? It is a useful near-surface approximation, not an identical local constant.

Is there no gravity in orbit? There is. Satellites undergo continuous free fall.

Does mass change with $h$? No. $P$ changes, not $m$.

Why is gravity stronger at the poles? Because centrifugal reduction is smaller and effective radius is shorter.

Does gravity rise toward Earth's center? Not in the uniform model; it decreases to zero.

Final synthesis

Earth's gravity decreases with $h$, varies slightly with $\phi$, and behaves differently in the interior. $m$ stays constant while $P$ follows local gravity. The correct model depends on domain and required precision.