[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]A particular and important case of circular orbit is the [i]geostationary orbit[/i]. A satellite in this orbit orbits in the plane of the equator with the same direction and the same period as the rotation of the Earth (23.93 hours). Viewed from Earth, the satellite occupies the same position in the celestial sphere at all times.[br][br]This period determines the distance to the center of the Earth (about 42,157 km, or approximately 35,786 km above the Earth's surface).[br][list][*][color=#999999]Note: The collection of geostationary satellites is also known as [/color][color=#cc0000][i]Clarke's Belt[/i][/color][color=#999999], as it was Arthur C. Clarke (a famous science fiction writer, author of 2001: A Space Odyssey) who first proposed the use of this orbit in 1945. [/color][br][/*][/list]Thus, the blue satellite will always be positioned directly overhead at the same point on the equator (we have chosen the intersection with the Greenwich meridian, that is, the point at longitude 0° and latitude 0°). To highlight this synchronization, we have represented a segment between the center of the Earth and the satellite.

[b]SCRIPT FOR SLIDER anima[/b][br][br][color=#cc0000][color=#cc0000]# Calculate the elapsed seconds dt; add one second if t1(1) < tt[/color][/color][br][color=#999999]SetValue(tt, t1(1))[br]SetValue(t1, First(GetTime(), 3))[br]SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000)[/color][br][br][color=#cc0000]# Rotate the Earth [color=#cc0000](f radians) [/color]and move M1, M2 and M3[/color] [br][color=#999999][color=#999999]SetValue[/color](f, f + ω dt)[br][color=#999999]SetValue[/color](M1, Rotate(M1, ω1 dt, axis1))[br][color=#999999]SetValue[/color](M2, [color=#999999]Rotate[/color](M2, ω2 dt, axis2))[br][color=#999999]SetValue[/color](M3, [color=#999999]Rotate[/color](M3, ω3 dt, axis3))[br][br][br][br][br][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][/color]