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Kepler's Third Law Formula

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

a semi = {(\frac{[GM.Earth]}{n^{2}})}^{\frac{1}{3}}

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

Kepler's Third Law Example

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Here is how the Kepler's Third Law equation looks like with Values.

Here is how the Kepler's Third Law equation looks like with Units.

Here is how the Kepler's Third Law equation looks like.

581706.9457 = {(\frac{4E+14}{{0.045}^{2}})}^{\frac{1}{3}}

581706.9457km = {(\frac{4E+14m³/s²}{{0.045rad/s}^{2}})}^{\frac{1}{3}}

581706.9457 = {(\frac{4E+14}{{0.045}^{2}})}^{\frac{1}{3}}

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Kepler's Third Law Solution

Follow our step by step solution on how to calculate Kepler's Third Law?

FIRST Step Consider the formula

a semi = {(\frac{[GM.Earth]}{n^{2}})}^{\frac{1}{3}}

Next Step Substitute values of Variables

∴

a semi = {(\frac{[GM.Earth]}{{0.045rad/s}^{2}})}^{\frac{1}{3}}

Next Step Substitute values of Constants

∴

a semi = {(\frac{4E+14m³/s²}{{0.045rad/s}^{2}})}^{\frac{1}{3}}

Next Step Prepare to Evaluate

∴

a semi = {(\frac{4E+14}{{0.045}^{2}})}^{\frac{1}{3}}

Next Step Evaluate

∴

a semi = 581706945.697113m

Next Step Convert to Output's Unit

∴

a semi = 581706.945697113km

LAST Step Rounding Answer

∴

a semi = 581706.9457km

Kepler's Third Law Formula Elements

Variables

Constants

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

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

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

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 Kepler's Third Law?

Kepler's Third Law evaluator uses Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3) to evaluate the Semi Major Axis, The Kepler's Third Law formula is defined as the squares of the orbital periods of the planets are directly proportional to the cubes of the semi-major axes of their orbits. Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. Semi Major Axis is denoted by a_semi symbol.

How to evaluate Kepler's Third Law using this online evaluator? To use this online evaluator for Kepler's Third Law, enter Mean Motion (n) and hit the calculate button.

FAQs on Kepler's Third Law

What is the formula to find Kepler's Third Law?

The formula of Kepler's Third Law is expressed as Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3). Here is an example- 0.581707 = ([GM.Earth]/0.045^2)^(1/3).

How to calculate Kepler's Third Law?

With Mean Motion (n) we can find Kepler's Third Law using the formula - Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3). This formula also uses Earth’s Geocentric Gravitational Constant .

Can the Kepler's Third Law be negative?

No, the Kepler's Third Law, measured in Length cannot be negative.

Which unit is used to measure Kepler's Third Law?

Kepler's Third Law is usually measured using the Kilometer[km] for Length. Meter[km], Millimeter[km], Decimeter[km] are the few other units in which Kepler's Third Law can be measured.

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