Kepler's First Law Calculator

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Satellite Orbital Characteristics

Geostationary Orbit

Radio Wave Propagation

✖The Semi major axis can be used to determine the size of satellite's orbit. It is half of the major axis.ⓘ Semi Major Axis [a_semi]			+10% -10%
✖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.ⓘ Semi Minor Axis [b_semi]			+10% -10%

✖Eccentricity refers to a characteristic of the orbit followed by a satellite around its primary body, typically the Earth.ⓘ Kepler's First Law [e]

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Formula

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Kepler's First Law

Formula

`"e" = sqrt(("a"_{"semi"}^2-"b"_{"semi"}^2))/"a"_{"semi"}`

Example

`"0.126863"=sqrt((("581.7km")^2-("577km")^2))/"581.7km"`

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Kepler's First Law Solution

STEP 0: Pre-Calculation Summary

Formula Used

Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis
e = sqrt((a_semi^2-b_semi^2))/a_semi
This formula uses 1 Functions, 3 Variables

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

Eccentricity - Eccentricity refers to a characteristic of the orbit followed by a satellite around its primary body, typically the Earth.
Semi Major Axis - (Measured in Meter) - The Semi major axis can be used to determine the size of satellite's orbit. It is half of the major axis.
Semi Minor Axis - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Semi Major Axis: 581.7 Kilometer --> 581700 Meter (Check conversion here)
Semi Minor Axis: 577 Kilometer --> 577000 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

e = sqrt((a_semi^2-b_semi^2))/a_semi --> sqrt((581700^2-577000^2))/581700

Evaluating ... ...

e = 0.126863114352173

STEP 3: Convert Result to Output's Unit

0.126863114352173 --> No Conversion Required

FINAL ANSWER

0.126863114352173 ≈ 0.126863 <-- Eccentricity

(Calculation completed in 00.020 seconds)

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Created by Shobhit Dimri

Bipin Tripathi Kumaon Institute of Technology (BTKIT), Dwarahat

Shobhit Dimri has created this Calculator and 900+ more calculators!

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Birsa Institute of Technology (BIT), Sindri

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< 16 Satellite Orbital Characteristics Calculators

Position Vector

Go Position Vector = (Major Axis*(1-Eccentricity^2))/(1+Eccentricity*cos(True Anomaly))

Kepler's First Law

Go Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis

Mean Anomaly

Go Mean Anomaly = Eccentric Anomaly-Eccentricity*sin(Eccentric Anomaly)

True Anomaly

Go True Anomaly = Mean Anomaly+(2*Eccentricity*sin(Mean Anomaly))

Universal Time

Go Universal Time = (1/24)*(Time in Hour+(Time in Minutes/60)+(Time in Seconds/3600))

Reference Time in Julian Centuries

Go Reference Time = (Julian Day-Julian Day Reference)/Julian Century

Julian Century

Go Julian Century = (Julian Day-Julian Day Reference)/Reference Time

Julian Day

Go Julian Day = (Reference Time*Julian Century)+Julian Day Reference

Nominal Mean Motion

Go Nominal Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3)

Mean Motion of Satellite

Go Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3)

Local Sidereal Time

Go Local Sidereal Time = Greenwich Sidereal Time+East Longitude

Kepler's Third Law

Go Semi Major Axis = ([GM.Earth]/Mean Motion^2)^(1/3)

Range Vector

Go Range Vector = Satellite Radius Vector-[Earth-R]

Orbital Period of Satellite in Minutes

Go Orbital Period in Minutes = 2*pi/Mean Motion

Anomalistic Period

Go Anomalistic Period = (2*pi)/Mean Motion

Universal Time Degree

Go Universal Time Degree = (Universal Time*360)

Kepler's First Law Formula

Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis
e = sqrt((a_semi^2-b_semi^2))/a_semi

Why is Kepler's first law important?

Kepler's First Law was a critical step in transforming our understanding of the solar system from the geocentric models of antiquity to the heliocentric model we accept today. It demonstrated the importance of empirical evidence, mathematical rigor, and observational data in advancing scientific knowledge.

How to Calculate Kepler's First Law?

Kepler's First Law calculator uses Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis to calculate 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 calculate Kepler's First Law using this online calculator? To use this online calculator for Kepler's First Law, enter Semi Major Axis (a_semi) & Semi Minor Axis (b_semi) and hit the calculate button. Here is how the Kepler's First Law calculation can be explained with given input values -> 0.99988 = sqrt((581700^2-577000^2))/581700.

FAQ

What is Kepler's First Law?

The Kepler's First Law formula is defined as that the path followed by a satellite around the primary will be an ellipse and is represented as e = sqrt((a_semi^2-b_semi^2))/a_semi or Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/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 & 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.

How to calculate Kepler's First Law?

The Kepler's First Law formula is defined as that the path followed by a satellite around the primary will be an ellipse is calculated using Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis. To calculate Kepler's First Law, you need Semi Major Axis (a_semi) & Semi Minor Axis (b_semi). With our tool, you need to enter the respective value for Semi Major Axis & Semi Minor Axis 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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