[color=#0000ff][i][color=#0000ff][i][color=#999999]This activity belongs to the GeoGebra book [url=https://www.geogebra.org/m/mes4bgft]The Domain of the Time[/url].[/color][/i][/color][/i][/color][br][br]Every mass alters the geometry of the space it occupies, creating a [i]gravity well[/i]. This well attracts everything around it toward its center of mass, with an acceleration that we call [i]gravitational acceleration[/i] or simply [i]gravity[/i].[br][br]In the case of Earth, its mass creates a gravitational force whose acceleration is denoted by [b][color=#6aa84f]g[/color][/b]. Therefore, [b][color=#6aa84f]g[/color][/b] is a vector pointing toward the center of the Earth, and its magnitude depends on the distance from the center of the Earth.[br][br]For masses located in space, the magnitude of [b][color=#6aa84f]g[/color][/b] is given by Newton's well-known formula:[br][center][math]\left|g\right|=G\frac{m_T_{ }}{d^2}[/math][/center]where G is the universal gravitational constant, [i]m[sub]T[/sub][/i] is the mass of the Earth, and [i]d[/i] is the distance from the center of the Earth.[br][br]This value is maximum at Earth's surface, gradually decreases as we move away from Earth, and also decreases as we move toward its center, becoming zero at the Earth's core. This is because, as we travel toward Earth's center, below the surface, the attraction from the mass already traversed becomes null (it is the sum of accelerations that cancel each other out by symmetry), so the effective mass [i][i]m[sub]T[/sub][/i][/i] being considered decreases. Since mass decreases proportionally to volume, and volume with the cube of distance [i]d[/i], the value of gravity decreases linearly (observe the straight part of the yellow graph).[br][br]This decrease would be truly linear if the Earth were a homogeneous sphere. However, the Earth's density is not constant, causing the decrease to not be linear (green graph). It also causes gravity to reach its maximum not at Earth's surface, but at the surface of the core, which is denser than the rest.[br][list][*]Note: Since Earth's radius is smaller at the poles than at the equator, the magnitude of [b][color=#6aa84f]g[/color][/b] is greater at the poles. Moreover, as we move from the poles to the equator, a small but progressively increasing portion of the [i]gravitational acceleration[/i] does not contribute to the weight of the mass but instead acts as [i]centripetal acceleration[/i] (or, in other words, it offsets the fictitious "centrifugal acceleration"). This prevents the mass from being lifted off Earth's surface, which is unnecessary at the poles where centripetal acceleration is zero. As a result of both factors, masses weigh about 0.5% more at the poles than at the equator.[/*][/list]In the following constructions, we will assume we are near Earth's surface ([i]d[/i] = [i]r[/i], where [i]r[/i] is Earth's average radius), so we approximate the value of the magnitude of [b][color=#6aa84f]g[/color][/b] to about 9.81 m/s².

[color=#999999][color=#999999][color=#0000ff][color=#0000ff][color=#999999][color=#999999]Author of the activity and GeoGebra construction: [/color][/color][/color][color=#0000ff][color=#999999][color=#999999][url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color][/color][/color][/color][/color][/color]