Gravity vs Gravitation

Author: Tianjiang Shuo
Website: https://cislunarspace.cn

Definition

Gravitation is the universal gravitational attraction exerted by the Earth on a space object, directed toward the geocenter, and depends only on the object's mass and geocentric distance. Gravity is the resultant force of gravitation and the centrifugal inertia force caused by Earth's rotation. When analyzing the motion of an object in a non-inertial coordinate system fixed to the Earth, gravity (not gravitation) must be used.

m\mathbf{g}' = m\mathbf{g} + m\mathbf{a}_e'

where $\mathbf{g}$ is the gravitational acceleration, $\mathbf{a}_e' = -\boldsymbol{\omega}_e \times (\boldsymbol{\omega}_e \times \mathbf{r})$ is the centrifugal acceleration, and $\mathbf{g}'$ is the gravity acceleration.

Core Elements

Comparison of Gravitation and Gravity

Characteristic	Gravitation	Gravity
Source	Universal gravitation	Gravitation + centrifugal inertia force
Direction	Toward the geocenter	Deviates from the geocenter (toward the equator)
Magnitude variation	Varies only with geocentric distance	Varies with geocentric distance and latitude
Applicable coordinate system	Inertial frame	Earth-fixed frame

Effect of Centrifugal Acceleration

Centrifugal acceleration lies in the meridian plane, perpendicular to the Earth's rotation axis and directed outward. Its radial and latitude components are:

\begin{cases} a_{er}' = r\omega_e^2 \cos^2\phi \\ a_{e\phi}' = -r\omega_e^2 \sin\phi\cos\phi \end{cases}

At the equator, the ratio of centrifugal acceleration to gravitational acceleration is $q \approx 3.46 \times 10^{-3}$ , on the same order of magnitude as the Earth's flattening $\alpha_e$ .

Gravity Acceleration Computation

The radial and latitude components of gravity acceleration are:

\begin{cases} g_r' = -\frac{fM}{r^2}\left[1 + J\left(\frac{a_e}{r}\right)^2(1 - 3\sin^2\phi) - q\left(\frac{r}{a_e}\right)^3\cos^2\phi\right] \\ g_\phi' = -\frac{fM}{r^2}\left[J\left(\frac{a_e}{r}\right)^2 + \frac{q}{2}\left(\frac{r}{a_e}\right)^3\right]\sin 2\phi \end{cases}

where $J$ is the zonal harmonic coefficient of the Earth's gravitational field.

Application Value

Correctly distinguishing between gravity and gravitation is fundamental to formulating vehicle equations of motion. In the launch frame (Earth-fixed frame), gravity acceleration is used; in the geocentric inertial frame, gravitational acceleration is used. Confusing the two leads to systematic errors in trajectory computation. For cislunar space missions, gravity must be used near the Earth; at greater distances from the Earth, the difference between the two becomes negligible.

References

Zheng Wei, An Xueying, Zhou Xiang, He Ruizhi. Aerospace Flight Mechanics (空天飞行力学)[M]. National University of Defense Technology, 2026.
Ren Xuan, Xiao Feng. Artificial Satellite Orbital Mechanics (人造地球卫星轨道力学)[M]. National University of Defense Technology Press.