Geo Radius Given Absolute Angular Velocity of Earth Calculator

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The Two Body Problem

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Circular Orbits

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Fundamental Parameters

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Geostationary Earth Satellite

Circular Orbit Parameters

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

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

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Formula

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Geo Radius Given Absolute Angular Velocity of Earth

Formula

`"R"_{"gso"} = ("[GM.Earth]"/"Ω"_{"E"}^2)^(1/3)`

Example

`"42164.17km"=("[GM.Earth]"/("7.2921159E^-05rad/s")^2)^(1/3)`

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Geo Radius Given Absolute Angular Velocity of Earth Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Constants Used

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

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Angular Speed of the Earth: 7.2921159E-05 Radian per Second --> 7.2921159E-05 Radian per Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_gso = ([GM.Earth]/Ω_E^2)^(1/3) --> ([GM.Earth]/7.2921159E-05^2)^(1/3)

Evaluating ... ...

R_gso = 42164169.4618618

STEP 3: Convert Result to Output's Unit

42164169.4618618 Meter -->42164.1694618618 Kilometer (Check conversion here)

FINAL ANSWER

42164.1694618618 ≈ 42164.17 Kilometer <-- Geostationary Radius

(Calculation completed in 00.004 seconds)

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Created by Harsh Raj

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

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National Institute Of Technology (NIT), Hamirpur

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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

Geo Radius Given Absolute Angular Velocity of Earth Formula

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

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 Geo Radius Given Absolute Angular Velocity of Earth?

Geo Radius Given Absolute Angular Velocity of Earth calculator uses Geostationary Radius = ([GM.Earth]/Angular Speed of the Earth^2)^(1/3) to calculate the Geostationary Radius, The Geo Radius Given Absolute Angular Velocity of Earth formula is defined as distance from the center of the Earth to the geostationary satellite's orbital location. It is a critical parameter for positioning geostationary satellites in orbits that synchronize with the Earth's rotation, allowing them to remain stationary relative to a specific point on the Earth's surface. Geostationary Radius is denoted by R_gso symbol.

How to calculate Geo Radius Given Absolute Angular Velocity of Earth using this online calculator? To use this online calculator for Geo Radius Given Absolute Angular Velocity of Earth, enter Angular Speed of the Earth (Ω_E) and hit the calculate button. Here is how the Geo Radius Given Absolute Angular Velocity of Earth calculation can be explained with given input values -> 42.16417 = ([GM.Earth]/7.2921159E-05^2)^(1/3).

FAQ

What is Geo Radius Given Absolute Angular Velocity of Earth?

The Geo Radius Given Absolute Angular Velocity of Earth formula is defined as distance from the center of the Earth to the geostationary satellite's orbital location. It is a critical parameter for positioning geostationary satellites in orbits that synchronize with the Earth's rotation, allowing them to remain stationary relative to a specific point on the Earth's surface and is represented as R_gso = ([GM.Earth]/Ω_E^2)^(1/3) or Geostationary Radius = ([GM.Earth]/Angular Speed of the Earth^2)^(1/3). Angular Speed of the Earth is the measure of how fast the central angle of a rotating body changes with respect to time.

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

The Geo Radius Given Absolute Angular Velocity of Earth formula is defined as distance from the center of the Earth to the geostationary satellite's orbital location. It is a critical parameter for positioning geostationary satellites in orbits that synchronize with the Earth's rotation, allowing them to remain stationary relative to a specific point on the Earth's surface is calculated using Geostationary Radius = ([GM.Earth]/Angular Speed of the Earth^2)^(1/3). To calculate Geo Radius Given Absolute Angular Velocity of Earth, you need Angular Speed of the Earth (Ω_E). With our tool, you need to enter the respective value for Angular Speed of the Earth 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 Geostationary Radius?

In this formula, Geostationary Radius uses Angular Speed of the Earth. We can use 2 other way(s) to calculate the same, which is/are as follows -

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

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