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Mean Motion of Satellite Formula

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Mean Motion is angular speed required for a body to complete an orbit, assuming constant speed in circular orbit that takes same time as variable speed elliptical orbit of actual body. Check FAQs

n = \sqrt{\frac{[GM.Earth]}{{a semi}^{3}}}

n - Mean Motion?a_semi - Semi Major Axis?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Mean Motion of Satellite Example

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With units

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Here is how the Mean Motion of Satellite equation looks like with Values.

Here is how the Mean Motion of Satellite equation looks like with Units.

Here is how the Mean Motion of Satellite equation looks like.

0.045 = \sqrt{\frac{4E+14}{{581.7}^{3}}}

0.045rad/s = \sqrt{\frac{4E+14m³/s²}{{581.7km}^{3}}}

0.045 = \sqrt{\frac{4E+14}{{581.7}^{3}}}

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Mean Motion of Satellite Solution

Follow our step by step solution on how to calculate Mean Motion of Satellite?

FIRST Step Consider the formula

n = \sqrt{\frac{[GM.Earth]}{{a semi}^{3}}}

Next Step Substitute values of Variables

∴

n = \sqrt{\frac{[GM.Earth]}{{581.7km}^{3}}}

Next Step Substitute values of Constants

∴

n = \sqrt{\frac{4E+14m³/s²}{{581.7km}^{3}}}

Next Step Convert Units

∴

n = \sqrt{\frac{4E+14m³/s²}{{581700m}^{3}}}

Next Step Prepare to Evaluate

∴

n = \sqrt{\frac{4E+14}{581700^{3}}}

Next Step Evaluate

∴

n = 0.0450008059755109rad/s

LAST Step Rounding Answer

∴

n = 0.045rad/s

Mean Motion of Satellite Formula Elements

Variables

Constants

Functions

Mean Motion

Mean Motion is angular speed required for a body to complete an orbit, assuming constant speed in circular orbit that takes same time as variable speed elliptical orbit of actual body.

Symbol: n

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Mean Motion

Semi Major Axis

The Semi major axis can be used to determine the size of satellite's orbit. It is half of the major axis.

Symbol: a_semi

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Semi Major Axis

Earth’s Geocentric Gravitational Constant

Earth’s Geocentric Gravitational Constant the gravitational parameter for the Earth as the central body.

Symbol: [GM.Earth]

Value: 3.986004418E+14 m³/s²

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.

Syntax: sqrt(Number)

Other formulas in Satellite Orbital Characteristics category

Go Anomalistic Period

T AP = \frac{2 \cdot π}{n}

Go Local Sidereal Time

LST = GST + E long

Go Mean Anomaly

M = E - e \cdot \sin (E)

Go Nominal Mean Motion

n o = \sqrt{\frac{[GM.Earth]}{{a semi}^{3}}}

How to Evaluate Mean Motion of Satellite?

Mean Motion of Satellite evaluator uses Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3) to evaluate the Mean Motion, The Mean Motion of Satellite formula is defined as the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body. Mean Motion is denoted by n symbol.

How to evaluate Mean Motion of Satellite using this online evaluator? To use this online evaluator for Mean Motion of Satellite, enter Semi Major Axis (a_semi) and hit the calculate button.

FAQs on Mean Motion of Satellite

What is the formula to find Mean Motion of Satellite?

The formula of Mean Motion of Satellite is expressed as Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3). Here is an example- 4.7E-6 = sqrt([GM.Earth]/581700^3).

How to calculate Mean Motion of Satellite?

With Semi Major Axis (a_semi) we can find Mean Motion of Satellite using the formula - Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3). This formula also uses Earth’s Geocentric Gravitational Constant and Square Root (sqrt) function(s).

Can the Mean Motion of Satellite be negative?

No, the Mean Motion of Satellite, measured in Angular Velocity cannot be negative.

Which unit is used to measure Mean Motion of Satellite?

Mean Motion of Satellite is usually measured using the Radian per Second[rad/s] for Angular Velocity. Radian per Day[rad/s], Radian per Hour[rad/s], Radian per Minute[rad/s] are the few other units in which Mean Motion of Satellite can be measured.

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