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Nominal Mean Motion Formula

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Nominal Mean Motion refers to the average rate at which a satellite orbits around a celestial body, such as the Earth. Check FAQs

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

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

Nominal Mean Motion Example

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With units

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

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

Here is how the Nominal Mean Motion 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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Nominal Mean Motion Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Substitute values of Constants

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

n o = 0.0450008059755109rad/s

LAST Step Rounding Answer

∴

n o = 0.045rad/s

Nominal Mean Motion Formula Elements

Variables

Constants

Functions

Nominal Mean Motion

Nominal Mean Motion refers to the average rate at which a satellite orbits around a celestial body, such as the Earth.

Symbol: n_o

Measurement: Angular VelocityUnit: rad/s

Note: Value should be greater than 0.

Formulas to find Nominal 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 Mean Motion of Satellite

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

How to Evaluate Nominal Mean Motion?

Nominal Mean Motion evaluator uses Nominal Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3) to evaluate the Nominal Mean Motion, The Nominal Mean Motion 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. Nominal Mean Motion is denoted by n_o symbol.

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

FAQs on Nominal Mean Motion

What is the formula to find Nominal Mean Motion?

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

How to calculate Nominal Mean Motion?

With Semi Major Axis (a_semi) we can find Nominal Mean Motion using the formula - Nominal 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 Nominal Mean Motion be negative?

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

Which unit is used to measure Nominal Mean Motion?

Nominal Mean Motion 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 Nominal Mean Motion can be measured.

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