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Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Formula

GoTime since Periapsis in Hyperbolic Orbit given Mean Anomaly Formula

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The Time since Periapsis is a measure of the duration that has passed since an object in orbit, such as a satellite, passed through its closest point to the central body, known as periapsis. Check FAQs

t = \frac{{h h}^{3}}{{[GM.Earth]}^{2} \cdot {({e h}^{2} - 1)}^{\frac{3}{2}}} \cdot (e h \cdot \sinh (F) - F)

t - Time since Periapsis?h_h - Angular Momentum of Hyperbolic Orbit?e_h - Eccentricity of Hyperbolic Orbit?F - Eccentric Anomaly in Hyperbolic Orbit?[GM.Earth] - Earth’s Geocentric Gravitational Constant?

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Example

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Here is how the Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly equation looks like.

2042.5091 = \frac{65700^{3}}{{4E+14}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot (1.339 \cdot \sinh (68.22) - 68.22)

2042.5091s = \frac{{65700km²/s}^{3}}{{4E+14m³/s²}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot (1.339 \cdot \sinh (68.22°) - 68.22°)

2042.5091 = \frac{65700^{3}}{{4E+14}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot (1.339 \cdot \sinh (68.22) - 68.22)

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Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Solution

Follow our step by step solution on how to calculate Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

FIRST Step Consider the formula

t = \frac{{h h}^{3}}{{[GM.Earth]}^{2} \cdot {({e h}^{2} - 1)}^{\frac{3}{2}}} \cdot (e h \cdot \sinh (F) - F)

Next Step Substitute values of Variables

∴

t = \frac{{65700km²/s}^{3}}{{[GM.Earth]}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot (1.339 \cdot \sinh (68.22°) - 68.22°)

Next Step Substitute values of Constants

∴

t = \frac{{65700km²/s}^{3}}{{4E+14m³/s²}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot (1.339 \cdot \sinh (68.22°) - 68.22°)

Next Step Convert Units

∴

t = \frac{{6.6E+10m²/s}^{3}}{{4E+14m³/s²}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot (1.339 \cdot \sinh (1.1907rad) - 1.1907rad)

Next Step Prepare to Evaluate

∴

t = \frac{{6.6E+10}^{3}}{{4E+14}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot (1.339 \cdot \sinh (1.1907) - 1.1907)

Next Step Evaluate

∴

t = 2042.50909767657s

LAST Step Rounding Answer

∴

t = 2042.5091s

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Formula Elements

Variables

Constants

Functions

Time since Periapsis

The Time since Periapsis is a measure of the duration that has passed since an object in orbit, such as a satellite, passed through its closest point to the central body, known as periapsis.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time since Periapsis

Angular Momentum of Hyperbolic Orbit

Angular Momentum of Hyperbolic Orbit is a fundamental physical quantity that characterizes the rotational motion of an object in orbit around a celestial body, such as a planet or a star.

Symbol: h_h

Measurement: Specific Angular MomentumUnit: km²/s

Note: Value should be greater than 0.

Formulas to find Angular Momentum of Hyperbolic Orbit

Eccentricity of Hyperbolic Orbit

Eccentricity of Hyperbolic Orbit describes how much the orbit differs from a perfect circle, and this value typically falls between 1 and infinity.

Symbol: e_h

Measurement: NAUnit: Unitless

Note: Value should be greater than 1.

Formulas to find Eccentricity of Hyperbolic Orbit

Eccentric Anomaly in Hyperbolic Orbit

Eccentric Anomaly in Hyperbolic Orbit is an angular parameter that characterizes the position of an object within its hyperbolic trajectory.

Symbol: F

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Eccentric Anomaly in Hyperbolic Orbit

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

sinh

The hyperbolic sine function, also known as the sinh function, is a mathematical function that is defined as the hyperbolic analogue of the sine function.

Syntax: sinh(Number)

Other Formulas to find Time since Periapsis

Go Time since Periapsis in Hyperbolic Orbit given Mean Anomaly

t = \frac{{h h}^{3}}{{[GM.Earth]}^{2} \cdot {({e h}^{2} - 1)}^{\frac{3}{2}}} \cdot M h

Other formulas in Orbital Position as Function of Time category

Go Mean Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

M h = e h \cdot \sinh (F) - F

Go Hyperbolic Eccentric Anomaly given Eccentricity and True Anomaly

F = 2 \cdot a \tanh (\sqrt{\frac{e h - 1}{e h + 1}} \cdot \tan (\frac{θ}{2}))

Go True Anomaly in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly and Eccentricity

θ = 2 \cdot a \tan (\sqrt{\frac{e h + 1}{e h - 1}} \cdot \tanh (\frac{F}{2}))

How to Evaluate Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly evaluator uses Time since Periapsis = Angular Momentum of Hyperbolic Orbit^3/([GM.Earth]^2*(Eccentricity of Hyperbolic Orbit^2-1)^(3/2))*(Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit) to evaluate the Time since Periapsis, The Time Since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly formula is defined as time that has elapsed since an object in a hyperbolic orbit passed through periapsis (the point of closest approach to the central body) based on the eccentric anomaly. Time since Periapsis is denoted by t symbol.

How to evaluate Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly using this online evaluator? To use this online evaluator for Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly, enter Angular Momentum of Hyperbolic Orbit (h_h), Eccentricity of Hyperbolic Orbit (e_h) & Eccentric Anomaly in Hyperbolic Orbit (F) and hit the calculate button.

FAQs on Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

What is the formula to find Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

The formula of Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly is expressed as Time since Periapsis = Angular Momentum of Hyperbolic Orbit^3/([GM.Earth]^2*(Eccentricity of Hyperbolic Orbit^2-1)^(3/2))*(Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit). Here is an example- 2042.509 = 65700000000^3/([GM.Earth]^2*(1.339^2-1)^(3/2))*(1.339*sinh(1.19066361571031)-1.19066361571031).

How to calculate Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

With Angular Momentum of Hyperbolic Orbit (h_h), Eccentricity of Hyperbolic Orbit (e_h) & Eccentric Anomaly in Hyperbolic Orbit (F) we can find Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly using the formula - Time since Periapsis = Angular Momentum of Hyperbolic Orbit^3/([GM.Earth]^2*(Eccentricity of Hyperbolic Orbit^2-1)^(3/2))*(Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit). This formula also uses Earth’s Geocentric Gravitational Constant and Hyperbolic Sine Function function(s).

What are the other ways to Calculate Time since Periapsis?

Here are the different ways to Calculate Time since Periapsis-

Time since Periapsis=Angular Momentum of Hyperbolic Orbit^3/([GM.Earth]^2*(Eccentricity of Hyperbolic Orbit^2-1)^(3/2))*Mean Anomaly in Hyperbolic Orbit

Can the Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly be negative?

No, the Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly, measured in Time cannot be negative.

Which unit is used to measure Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly can be measured.

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Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Formula

​GoTime since Periapsis in Hyperbolic Orbit given Mean Anomaly Formula

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Example

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Solution

Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Formula Elements

Other Formulas to find Time since Periapsis

Other formulas in Orbital Position as Function of Time category

How to Evaluate Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly?

FAQs on Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

Variable Name

GoTime since Periapsis in Hyperbolic Orbit given Mean Anomaly Formula