Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period Calculator

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The Two Body Problem

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Elliptical Orbits

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Orbital Position as Function of Time

Elliptical Orbit Parameters

✖The Eccentric Anomaly is an angular parameter that defines the position of a body that is moving along an Kepler orbit.ⓘ Eccentric Anomaly [E]			+10% -10%
✖Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.ⓘ Eccentricity of Elliptical Orbit [e_e]			+10% -10%
✖The time period of Elliptic Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.ⓘ Time Period of Elliptic Orbit [T_e]			+10% -10%

✖The Time since Periapsis in Elliptical Orbit is a measure of the duration that has passed since an object in orbit, passed through its closest point to the central body, known as periapsis.ⓘ Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period [t_e]

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Formula

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Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period

Formula

`"t"_{"e"} = ("E"-"e"_{"e"}*sin("E"))*"T"_{"e"}/(2*Pi(6))`

Example

`"4284.393s"=("101°"-"0.6"*sin("101°"))*"21900s"/(2*Pi(6))`

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Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time since Periapsis in Elliptical Orbit = (Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly))*Time Period of Elliptic Orbit/(2*Pi(6))
t_e = (E-e_e*sin(E))*T_e/(2*Pi(6))
This formula uses 2 Functions, 4 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
Pi - The prime-counting function is a function in mathematics that counts the number of prime numbers that are less than or equal to a given real number., Pi(Number)

Variables Used

Time since Periapsis in Elliptical Orbit - (Measured in Second) - The Time since Periapsis in Elliptical Orbit is a measure of the duration that has passed since an object in orbit, passed through its closest point to the central body, known as periapsis.
Eccentric Anomaly - (Measured in Radian) - The Eccentric Anomaly is an angular parameter that defines the position of a body that is moving along an Kepler orbit.
Eccentricity of Elliptical Orbit - Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.
Time Period of Elliptic Orbit - (Measured in Second) - The time period of Elliptic Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.

STEP 1: Convert Input(s) to Base Unit

Eccentric Anomaly: 101 Degree --> 1.76278254451394 Radian (Check conversion here)
Eccentricity of Elliptical Orbit: 0.6 --> No Conversion Required
Time Period of Elliptic Orbit: 21900 Second --> 21900 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t_e = (E-e_e*sin(E))*T_e/(2*Pi(6)) --> (1.76278254451394-0.6*sin(1.76278254451394))*21900/(2*Pi(6))

Evaluating ... ...

t_e = 4284.39275572536

STEP 3: Convert Result to Output's Unit

4284.39275572536 Second --> No Conversion Required

FINAL ANSWER

4284.39275572536 ≈ 4284.393 Second <-- Time since Periapsis in Elliptical Orbit

(Calculation completed in 00.004 seconds)

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< 6 Orbital Position as Function of Time Calculators

Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period

Go Time since Periapsis in Elliptical Orbit = (Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly))*Time Period of Elliptic Orbit/(2*Pi(6))

Eccentric Anomaly in Elliptic Orbit given True Anomaly and Eccentricity

Go Eccentric Anomaly = 2*atan(sqrt((1-Eccentricity of Elliptical Orbit)/(1+Eccentricity of Elliptical Orbit))*tan(True Anomaly in Elliptical Orbit/2))

True Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity

Go True Anomaly in Elliptical Orbit = 2*atan(sqrt((1+Eccentricity of Elliptical Orbit)/(1-Eccentricity of Elliptical Orbit))*tan(Eccentric Anomaly/2))

Mean Anomaly in Elliptic Orbit given Eccentric Anomaly and Eccentricity

Go Mean Anomaly in Elliptical Orbit = Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly)

Time since Periapsis in Elliptic Orbit given Mean Anomaly

Go Time since Periapsis in Elliptical Orbit = Mean Anomaly in Elliptical Orbit*Time Period of Elliptic Orbit/(2*pi)

Mean Anomaly in Elliptic Orbit given Time since Periapsis

Go Mean Anomaly in Elliptical Orbit = (2*pi*Time since Periapsis in Elliptical Orbit)/Time Period of Elliptic Orbit

Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period Formula

Time since Periapsis in Elliptical Orbit = (Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly))*Time Period of Elliptic Orbit/(2*Pi(6))
t_e = (E-e_e*sin(E))*T_e/(2*Pi(6))

Geometric Visualization of Eccentric Anamoly

The eccentric anomaly, E, is the angle between the direction of periapsis and the current position of an object on its orbit, projected onto the ellipse's Page 10 circumscribing circle perpendicularly to the major axis, measured at the center of the ellipse.

How to Calculate Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period?

Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period calculator uses Time since Periapsis in Elliptical Orbit = (Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly))*Time Period of Elliptic Orbit/(2*Pi(6)) to calculate the Time since Periapsis in Elliptical Orbit, The Time Since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period formula is defined as the time that has elapsed since an object in an elliptic orbit passed through periapsis (the point of closest approach to the central body) based on the eccentric anomaly. Time since Periapsis in Elliptical Orbit is denoted by t_e symbol.

How to calculate Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period using this online calculator? To use this online calculator for Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period, enter Eccentric Anomaly (E), Eccentricity of Elliptical Orbit (e_e) & Time Period of Elliptic Orbit (T_e) and hit the calculate button. Here is how the Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period calculation can be explained with given input values -> 4284.393 = (1.76278254451394-0.6*sin(1.76278254451394))*21900/(2*Pi(6)).

FAQ

What is Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period?

The Time Since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period formula is defined as the time that has elapsed since an object in an elliptic orbit passed through periapsis (the point of closest approach to the central body) based on the eccentric anomaly and is represented as t_e = (E-e_e*sin(E))*T_e/(2*Pi(6)) or Time since Periapsis in Elliptical Orbit = (Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly))*Time Period of Elliptic Orbit/(2*Pi(6)). The Eccentric Anomaly is an angular parameter that defines the position of a body that is moving along an Kepler orbit, Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is & The time period of Elliptic Orbit is the amount of time a given astronomical object takes to complete one orbit around another object.

How to calculate Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period?

The Time Since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period formula is defined as the time that has elapsed since an object in an elliptic orbit passed through periapsis (the point of closest approach to the central body) based on the eccentric anomaly is calculated using Time since Periapsis in Elliptical Orbit = (Eccentric Anomaly-Eccentricity of Elliptical Orbit*sin(Eccentric Anomaly))*Time Period of Elliptic Orbit/(2*Pi(6)). To calculate Time since Periapsis in Elliptic Orbit given Eccentric Anomaly and Time Period, you need Eccentric Anomaly (E), Eccentricity of Elliptical Orbit (e_e) & Time Period of Elliptic Orbit (T_e). With our tool, you need to enter the respective value for Eccentric Anomaly, Eccentricity of Elliptical Orbit & Time Period of Elliptic Orbit and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Time since Periapsis in Elliptical Orbit?

In this formula, Time since Periapsis in Elliptical Orbit uses Eccentric Anomaly, Eccentricity of Elliptical Orbit & Time Period of Elliptic Orbit. We can use 1 other way(s) to calculate the same, which is/are as follows -

Time since Periapsis in Elliptical Orbit = Mean Anomaly in Elliptical Orbit*Time Period of Elliptic Orbit/(2*pi)

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