Speed of Satellite in Circular LEO as Function of Altitude Calculator

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The Two Body Problem

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Circular Orbit Parameters

Geostationary Earth Satellite

✖Height of Satellite is the distance between the satellite's position above the Earth's surface and the Earth's surface itself.ⓘ Height of Satellite [z]

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✖Speed of Satellite is the rate at which a satellite travels in its orbit around a celestial body, such as Earth.ⓘ Speed of Satellite in Circular LEO as Function of Altitude [v]

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Formula

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Speed of Satellite in Circular LEO as Function of Altitude

Formula

`"v" = sqrt("[GM.Earth]"/("[Earth-R]"+"z"))`

Example

`"3.142202km/s"=sqrt("[GM.Earth]"/("[Earth-R]"+"34000km"))`

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Speed of Satellite in Circular LEO as Function of Altitude Solution

STEP 0: Pre-Calculation Summary

Formula Used

Speed of Satellite = sqrt([GM.Earth]/([Earth-R]+Height of Satellite))
v = sqrt([GM.Earth]/([Earth-R]+z))
This formula uses 2 Constants, 1 Functions, 2 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14
[Earth-R] - Earth mean radius Value Taken As 6371.0088

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

Speed of Satellite - (Measured in Meter per Second) - Speed of Satellite is the rate at which a satellite travels in its orbit around a celestial body, such as Earth.
Height of Satellite - (Measured in Meter) - Height of Satellite is the distance between the satellite's position above the Earth's surface and the Earth's surface itself.

STEP 1: Convert Input(s) to Base Unit

Height of Satellite: 34000 Kilometer --> 34000000 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v = sqrt([GM.Earth]/([Earth-R]+z)) --> sqrt([GM.Earth]/([Earth-R]+34000000))

Evaluating ... ...

v = 3142.20190054288

STEP 3: Convert Result to Output's Unit

3142.20190054288 Meter per Second -->3.14220190054288 Kilometer per Second (Check conversion here)

FINAL ANSWER

3.14220190054288 ≈ 3.142202 Kilometer per Second <-- Speed of Satellite

(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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< 11 Circular Orbit Parameters Calculators

Orbital Period

Go Time Period of Orbit = 2*pi*sqrt((Orbit Radius^3)/([G.]*Central Body Mass))

Circular Orbital Radius Given Time Period of Circular Orbit

Go Orbit Radius = ((Time Period of Orbit*sqrt([GM.Earth]))/(2*pi))^(2/3)

Speed of Satellite in Circular LEO as Function of Altitude

Go Speed of Satellite = sqrt([GM.Earth]/([Earth-R]+Height of Satellite))

Time Period of Circular Orbit

Go Time Period of Orbit = (2*pi*Orbit Radius^(3/2))/(sqrt([GM.Earth]))

Velocity of Circular Orbit

Go Velocity of Circular Orbit = sqrt([GM.Earth]/Orbit Radius)

Circular Orbital Radius

Go Orbit Radius = Angular Momentum of Circular Orbit^2/[GM.Earth]

Specific Energy of Circular Orbit Given Orbital Radius

Go Specific Energy of Orbit = -([GM.Earth])/(2*Orbit Radius)

Orbital Radius Given Specific Energy of Circular Orbit

Go Orbit Radius = -([GM.Earth])/(2*Specific Energy of Orbit)

Circular Orbital Radius Given Velocity of Circular Orbit

Go Orbit Radius = [GM.Earth]/Velocity of Circular Orbit^2

Specific Energy of Circular Orbit

Go Specific Energy of Orbit = -([GM.Earth]^2)/(2*Angular Momentum of Circular Orbit^2)

Escape Velocity given Speed of Satellite in Circular Orbit

Go Escape Velocity = sqrt(2)*Velocity of Circular Orbit

Speed of Satellite in Circular LEO as Function of Altitude Formula

Speed of Satellite = sqrt([GM.Earth]/([Earth-R]+Height of Satellite))
v = sqrt([GM.Earth]/([Earth-R]+z))

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 Speed of Satellite in Circular LEO as Function of Altitude?

Speed of Satellite in Circular LEO as Function of Altitude calculator uses Speed of Satellite = sqrt([GM.Earth]/([Earth-R]+Height of Satellite)) to calculate the Speed of Satellite, The Speed of Satellite in Circular LEO as Function of Altitude formula is defined as velocity at which a satellite orbits the Earth, taking into account its altitude from the Earth's surface and the gravitational constant of the Earth. Speed of Satellite is denoted by v symbol.

How to calculate Speed of Satellite in Circular LEO as Function of Altitude using this online calculator? To use this online calculator for Speed of Satellite in Circular LEO as Function of Altitude, enter Height of Satellite (z) and hit the calculate button. Here is how the Speed of Satellite in Circular LEO as Function of Altitude calculation can be explained with given input values -> 0.007847 = sqrt([GM.Earth]/([Earth-R]+height_of_satellite)).

FAQ

What is Speed of Satellite in Circular LEO as Function of Altitude?

The Speed of Satellite in Circular LEO as Function of Altitude formula is defined as velocity at which a satellite orbits the Earth, taking into account its altitude from the Earth's surface and the gravitational constant of the Earth and is represented as v = sqrt([GM.Earth]/([Earth-R]+z)) or Speed of Satellite = sqrt([GM.Earth]/([Earth-R]+Height of Satellite)). Height of Satellite is the distance between the satellite's position above the Earth's surface and the Earth's surface itself.

How to calculate Speed of Satellite in Circular LEO as Function of Altitude?

The Speed of Satellite in Circular LEO as Function of Altitude formula is defined as velocity at which a satellite orbits the Earth, taking into account its altitude from the Earth's surface and the gravitational constant of the Earth is calculated using Speed of Satellite = sqrt([GM.Earth]/([Earth-R]+Height of Satellite)). To calculate Speed of Satellite in Circular LEO as Function of Altitude, you need Height of Satellite (z). With our tool, you need to enter the respective value for Height of Satellite and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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