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Time since Periapsis in Hyperbolic Orbit given Mean Anomaly Formula

GoTime since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric 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 M h

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

Time since Periapsis in Hyperbolic Orbit given Mean Anomaly Example

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

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

2042.3973 = \frac{65700^{3}}{{4E+14}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot 46.29

2042.3973s = \frac{{65700km²/s}^{3}}{{4E+14m³/s²}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot 46.29°

2042.3973 = \frac{65700^{3}}{{4E+14}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot 46.29

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Time since Periapsis in Hyperbolic Orbit given Mean Anomaly Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

t = \frac{{65700km²/s}^{3}}{{[GM.Earth]}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot 46.29°

Next Step Substitute values of Constants

∴

t = \frac{{65700km²/s}^{3}}{{4E+14m³/s²}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot 46.29°

Next Step Convert Units

∴

t = \frac{{6.6E+10m²/s}^{3}}{{4E+14m³/s²}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot 0.8079rad

Next Step Prepare to Evaluate

∴

t = \frac{{6.6E+10}^{3}}{{4E+14}^{2} \cdot {({1.339}^{2} - 1)}^{\frac{3}{2}}} \cdot 0.8079

Next Step Evaluate

∴

t = 2042.39729017283s

LAST Step Rounding Answer

∴

t = 2042.3973s

Time since Periapsis in Hyperbolic Orbit given Mean Anomaly Formula Elements

Variables

Constants

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

Mean Anomaly in Hyperbolic Orbit

The Mean Anomaly in Hyperbolic Orbit is a time-related parameter that represents the angular distance covered by an object in its hyperbolic trajectory since passing through periapsis.

Symbol: M_h

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Mean 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

Other Formulas to find Time since Periapsis

Go Time since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly

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

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 Mean Anomaly?

Time since Periapsis in Hyperbolic Orbit given Mean Anomaly evaluator uses 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 to evaluate the Time since Periapsis, Time since Periapsis in Hyperbolic Orbit given Mean Anomaly formula is defined as a method to determine the elapsed time since the closest approach of an object in a hyperbolic trajectory, based on its mean anomaly and orbital parameters. Time since Periapsis is denoted by t symbol.

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

FAQs on Time since Periapsis in Hyperbolic Orbit given Mean Anomaly

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

The formula of Time since Periapsis in Hyperbolic Orbit given Mean Anomaly is expressed as 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. Here is an example- 2042.397 = 65700000000^3/([GM.Earth]^2*(1.339^2-1)^(3/2))*0.807912910748023.

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

With Angular Momentum of Hyperbolic Orbit (h_h), Eccentricity of Hyperbolic Orbit (e_h) & Mean Anomaly in Hyperbolic Orbit (M_h) we can find Time since Periapsis in Hyperbolic Orbit given Mean Anomaly using the formula - 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. This formula also uses Earth’s Geocentric Gravitational Constant .

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))*(Eccentricity of Hyperbolic Orbit*sinh(Eccentric Anomaly in Hyperbolic Orbit)-Eccentric Anomaly in Hyperbolic Orbit)

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

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

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

Time since Periapsis in Hyperbolic Orbit given Mean 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 Mean Anomaly can be measured.

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Time since Periapsis in Hyperbolic Orbit given Mean Anomaly Formula

​GoTime since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Formula

Time since Periapsis in Hyperbolic Orbit given Mean Anomaly Example

Time since Periapsis in Hyperbolic Orbit given Mean Anomaly Solution

Time since Periapsis in Hyperbolic Orbit given Mean 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 Mean Anomaly?

FAQs on Time since Periapsis in Hyperbolic Orbit given Mean Anomaly

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GoTime since Periapsis in Hyperbolic Orbit given Hyperbolic Eccentric Anomaly Formula