Absolute Angular Velocity of Earth Given Geo Radius Calculator

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The Two Body Problem

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Fundamental Parameters

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Geostationary Earth Satellite

Circular Orbit Parameters

✖Geostationary Radius refers to the distance between the Earth's surface and a geostationary satellite in orbit around the Earth.ⓘ Geostationary Radius [R_gso]

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✖Angular Speed of the Earth is the measure of how fast the central angle of a rotating body changes with respect to time.ⓘ Absolute Angular Velocity of Earth Given Geo Radius [Ω_E]

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Formula

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Absolute Angular Velocity of Earth Given Geo Radius

Formula

`"Ω"_{"E"} = sqrt("[GM.Earth]"/"R"_{"gso"}^3)`

Example

`"7.3E^-5rad/s"=sqrt("[GM.Earth]"/("42164.17km")^3)`

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Absolute Angular Velocity of Earth Given Geo Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angular Speed of the Earth = sqrt([GM.Earth]/Geostationary Radius^3)
Ω_E = sqrt([GM.Earth]/R_gso^3)
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Angular Speed of the Earth - (Measured in Radian per Second) - Angular Speed of the Earth is the measure of how fast the central angle of a rotating body changes with respect to time.
Geostationary Radius - (Measured in Meter) - Geostationary Radius refers to the distance between the Earth's surface and a geostationary satellite in orbit around the Earth.

STEP 1: Convert Input(s) to Base Unit

Geostationary Radius: 42164.17 Kilometer --> 42164170 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Ω_E = sqrt([GM.Earth]/R_gso^3) --> sqrt([GM.Earth]/42164170^3)

Evaluating ... ...

Ω_E = 7.29211576039691E-05

STEP 3: Convert Result to Output's Unit

7.29211576039691E-05 Radian per Second --> No Conversion Required

FINAL ANSWER

7.29211576039691E-05 ≈ 7.3E-5 Radian per Second <-- Angular Speed of the Earth

(Calculation completed in 00.004 seconds)

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Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

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< 7 Geostationary Earth Satellite Calculators

Absolute Angular Velocity of Earth Given Geo Radius

Go Angular Speed of the Earth = sqrt([GM.Earth]/Geostationary Radius^3)

Speed of Satellite in its Circular GEO of Radius

Go Speed of Satellite = sqrt([GM.Earth]/(Geostationary Radius))

Geo Radius Given Absolute Angular Velocity of Earth

Go Geostationary Radius = ([GM.Earth]/Angular Speed of the Earth^2)^(1/3)

Geo Speed along its Circular Path Given Absolute Angular Velocity of Earth

Go Speed of Satellite = Angular Speed of the Earth*Geostationary Radius

Geo Radius Given Absolute Angular Velocity of Earth and Geo Speed

Go Geostationary Radius = Speed of Satellite/Angular Speed of the Earth

Absolute Angular Velocity Given Geo Radius of Earth and Geo Speed

Go Angular Speed of the Earth = Speed of Satellite/Geostationary Radius

Geo Radius Given Speed of Satellite in its Circular Geo Orbit

Go Geostationary Radius = [GM.Earth]/Speed of Satellite^2

Absolute Angular Velocity of Earth Given Geo Radius Formula

Angular Speed of the Earth = sqrt([GM.Earth]/Geostationary Radius^3)
Ω_E = sqrt([GM.Earth]/R_gso^3)

Kepler's Laws and Gravitational Attraction

Johannes Kepler's laws of planetary motion, developed in the 17th century, provided significant insights into the relationship between celestial bodies and gravity. Kepler's laws describe the elliptical orbits of planets and other objects in the solar system, all of which are governed by the gravitational pull of the central body, such as the Sun. These laws laid the foundation for understanding how gravity affects the motion of objects in space, paving the way for Sir Isaac Newton's formulation of the law of universal gravitation.

How to Calculate Absolute Angular Velocity of Earth Given Geo Radius?

Absolute Angular Velocity of Earth Given Geo Radius calculator uses Angular Speed of the Earth = sqrt([GM.Earth]/Geostationary Radius^3) to calculate the Angular Speed of the Earth, The Absolute Angular Velocity of Earth Given Geo Radius formula is defined as measure of Earth's rotation rate, expressed in units like radians per second (rad/s) or degrees per hour (°/hr). Angular Speed of the Earth is denoted by Ω_E symbol.

How to calculate Absolute Angular Velocity of Earth Given Geo Radius using this online calculator? To use this online calculator for Absolute Angular Velocity of Earth Given Geo Radius, enter Geostationary Radius (R_gso) and hit the calculate button. Here is how the Absolute Angular Velocity of Earth Given Geo Radius calculation can be explained with given input values -> 0.001138 = sqrt([GM.Earth]/42164170^3).

FAQ

What is Absolute Angular Velocity of Earth Given Geo Radius?

The Absolute Angular Velocity of Earth Given Geo Radius formula is defined as measure of Earth's rotation rate, expressed in units like radians per second (rad/s) or degrees per hour (°/hr) and is represented as Ω_E = sqrt([GM.Earth]/R_gso^3) or Angular Speed of the Earth = sqrt([GM.Earth]/Geostationary Radius^3). Geostationary Radius refers to the distance between the Earth's surface and a geostationary satellite in orbit around the Earth.

How to calculate Absolute Angular Velocity of Earth Given Geo Radius?

The Absolute Angular Velocity of Earth Given Geo Radius formula is defined as measure of Earth's rotation rate, expressed in units like radians per second (rad/s) or degrees per hour (°/hr) is calculated using Angular Speed of the Earth = sqrt([GM.Earth]/Geostationary Radius^3). To calculate Absolute Angular Velocity of Earth Given Geo Radius, you need Geostationary Radius (R_gso). With our tool, you need to enter the respective value for Geostationary Radius and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Angular Speed of the Earth?

In this formula, Angular Speed of the Earth uses Geostationary Radius. We can use 1 other way(s) to calculate the same, which is/are as follows -

Angular Speed of the Earth = Speed of Satellite/Geostationary Radius

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