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((asemi^2-bsemi^2))/asemi
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((asemi^2-bsemi^2))/asemi --> 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
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Satellite Orbital Characteristics Calculators

Mean Anomaly
​ LaTeX ​ Go Mean Anomaly = Eccentric Anomaly-Eccentricity*sin(Eccentric Anomaly)
Mean Motion of Satellite
​ LaTeX ​ Go Mean Motion = sqrt([GM.Earth]/Semi Major Axis^3)
Local Sidereal Time
​ LaTeX ​ Go Local Sidereal Time = Greenwich Sidereal Time+East Longitude
Anomalistic Period
​ LaTeX ​ Go Anomalistic Period = (2*pi)/Mean Motion

Kepler's First Law Formula

​LaTeX ​Go
Eccentricity = sqrt((Semi Major Axis^2-Semi Minor Axis^2))/Semi Major Axis
e = sqrt((asemi^2-bsemi^2))/asemi

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 (asemi) & Semi Minor Axis (bsemi) 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((asemi^2-bsemi^2))/asemi 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 (asemi) & Semi Minor Axis (bsemi). 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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