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Kepler's First Law Formula

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Eccentricity refers to a characteristic of the orbit followed by a satellite around its primary body, typically the Earth. Check FAQs

e = \frac{\sqrt{({a semi}^{2} - {b semi}^{2})}}{a semi}

e - Eccentricity?a_semi - Semi Major Axis?b_semi - Semi Minor Axis?

Kepler's First Law Example

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

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

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

0.1269 = \frac{\sqrt{({581.7}^{2} - 577^{2})}}{581.7}

0.1269 = \frac{\sqrt{({581.7km}^{2} - {577km}^{2})}}{581.7km}

0.1269 = \frac{\sqrt{({581.7}^{2} - 577^{2})}}{581.7}

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Kepler's First Law Solution

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

FIRST Step Consider the formula

e = \frac{\sqrt{({a semi}^{2} - {b semi}^{2})}}{a semi}

Next Step Substitute values of Variables

∴

e = \frac{\sqrt{({581.7km}^{2} - {577km}^{2})}}{581.7km}

Next Step Convert Units

∴

e = \frac{\sqrt{({581700m}^{2} - {577000m}^{2})}}{581700m}

Next Step Prepare to Evaluate

∴

e = \frac{\sqrt{(581700^{2} - 577000^{2})}}{581700}

Next Step Evaluate

∴

e = 0.126863114352173

LAST Step Rounding Answer

∴

e = 0.1269

Kepler's First Law Formula Elements

Variables

Functions

Eccentricity

Eccentricity refers to a characteristic of the orbit followed by a satellite around its primary body, typically the Earth.

Symbol: e

Measurement: NAUnit: Unitless

Note: Value should be between 0 to 1.

Formulas to find Eccentricity

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

Semi Minor Axis

Semi Minor axis is a line segment that is at right angles with the semi-major axis and has one end at the center of the conic section.

Symbol: b_semi

Measurement: LengthUnit: km

Note: Value should be greater than 0.

Formulas to find Semi Minor Axis

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 Kepler's First Law?

Kepler's First Law evaluator uses Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis to evaluate the Eccentricity, The Kepler's First Law formula is defined as that the path followed by a satellite around the primary will be an ellipse. Eccentricity is denoted by e symbol.

How to evaluate Kepler's First Law using this online evaluator? To use this online evaluator for Kepler's First Law, enter Semi Major Axis (a_semi) & Semi Minor Axis (b_semi) and hit the calculate button.

FAQs on Kepler's First Law

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

The formula of Kepler's First Law is expressed as Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis. Here is an example- 0.99988 = sqrt((581700^2-577000^2))/581700.

How to calculate Kepler's First Law?

With Semi Major Axis (a_semi) & Semi Minor Axis (b_semi) we can find Kepler's First Law using the formula - Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis. This formula also uses Square Root (sqrt) function(s).

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