Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum Calculator

⤿

The Two Body Problem

⤿

Elliptical Orbits

Circular Orbits

Fundamental Parameters

Hyperbolic Orbits

Parabolic Orbits

⤿

Elliptical Orbit Parameters

Orbital Position as Function of Time

✖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%
✖True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit.ⓘ True Anomaly in Elliptical Orbit [θ_e]			+10% -10%
✖Angular Momentum of Elliptic 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.ⓘ Angular Momentum of Elliptic Orbit [h_e]			+10% -10%

✖Radial Velocity of Satellite is the component of its velocity that is directed along the line of sight from an observer on the Earth's surface.ⓘ Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum [v_r]

⎘ Copy

👎

Formula

✖

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum

Formula

`"v"_{"r"} = "[GM.Earth]"*"e"_{"e"}*sin("θ"_{"e"})/"h"_{"e"}`

Example

`"2.567101km/s"="[GM.Earth]"*"0.6"*sin("135.11°")/"65750km²/s"`

Calculator

LaTeX

Reset

👍

Download Elliptical Orbits Formulas PDF PDF Image

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit
v_r = [GM.Earth]*e_e*sin(θ_e)/h_e
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

[GM.Earth] - Earth’s Geocentric Gravitational Constant Value Taken As 3.986004418E+14

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)

Variables Used

Radial Velocity of Satellite - (Measured in Meter per Second) - Radial Velocity of Satellite is the component of its velocity that is directed along the line of sight from an observer on the Earth's surface.
Eccentricity of Elliptical Orbit - Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is.
True Anomaly in Elliptical Orbit - (Measured in Radian) - True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit.
Angular Momentum of Elliptic Orbit - (Measured in Squaer Meter per Second) - Angular Momentum of Elliptic 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.

STEP 1: Convert Input(s) to Base Unit

Eccentricity of Elliptical Orbit: 0.6 --> No Conversion Required
True Anomaly in Elliptical Orbit: 135.11 Degree --> 2.3581143523691 Radian (Check conversion here)
Angular Momentum of Elliptic Orbit: 65750 Square Kilometer per Second --> 65750000000 Squaer Meter per Second (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

v_r = [GM.Earth]*e_e*sin(θ_e)/h_e --> [GM.Earth]*0.6*sin(2.3581143523691)/65750000000

Evaluating ... ...

v_r = 2567.10056776404

STEP 3: Convert Result to Output's Unit

2567.10056776404 Meter per Second -->2.56710056776404 Kilometer per Second (Check conversion here)

FINAL ANSWER

2.56710056776404 ≈ 2.567101 Kilometer per Second <-- Radial Velocity of Satellite

(Calculation completed in 00.004 seconds)

You are here -

Home » Physics » Orbital Mechanics » The Two Body Problem » Elliptical Orbits » Elliptical Orbit Parameters » Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum

Credits

Created by Harsh Raj

Indian Institute of Technology, Kharagpur (IIT KGP), West Bengal

Harsh Raj has created this Calculator and 50+ more calculators!

Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

Kartikay Pandit has verified this Calculator and 400+ more calculators!

< 17 Elliptical Orbit Parameters Calculators

True Anomaly in Elliptic Orbit Given Radial Position, Eccentricity, and Angular Momentum

Go True Anomaly in Elliptical Orbit = acos((Angular Momentum of Elliptic Orbit^2/([GM.Earth]*Radial Position in Elliptical Orbit)-1)/Eccentricity of Elliptical Orbit)

Time Period of Elliptical Orbit given Semi-Major Axis

Go Time Period of Elliptic Orbit = 2*pi*Semi Major Axis of Elliptic Orbit^2*sqrt(1-Eccentricity of Elliptical Orbit^2)/Angular Momentum of Elliptic Orbit

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum

Go Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit

Eccentricity of Elliptical Orbit given Apogee and Perigee

Go Eccentricity of Elliptical Orbit = (Apogee Radius in Elliptic Orbit-Perigee Radius in Elliptic Orbit)/(Apogee Radius in Elliptic Orbit+Perigee Radius in Elliptic Orbit)

Time Period for One Complete Revolution given Angular Momentum

Go Time Period of Elliptic Orbit = (2*pi*Semi Major Axis of Elliptic Orbit*Semi Minor Axis of Elliptic Orbit)/Angular Momentum of Elliptic Orbit

Elliptical Orbit Time Period given Angular Momentum and Eccentricity

Go Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3

Time Period of Elliptical Orbit given Angular Momentum

Go Time Period of Elliptic Orbit = (2*pi)/[GM.Earth]^2*(Angular Momentum of Elliptic Orbit/sqrt(1-Eccentricity of Elliptical Orbit^2))^3

Apogee Radius of Elliptic Orbit Given Angular Momentum and Eccentricity

Go Apogee Radius in Elliptic Orbit = Angular Momentum of Elliptic Orbit^2/([GM.Earth]*(1-Eccentricity of Elliptical Orbit))

Specific Energy of Elliptic Orbit given Angular Momentum

Go Specific Energy of Elliptical Orbit = -1/2*[GM.Earth]^2/Angular Momentum of Elliptic Orbit^2*(1-Eccentricity of Elliptical Orbit^2)

Azimuth-Averaged Radius Given Apogee and Perigee Radii

Go Azimuth Averaged Radius = sqrt(Apogee Radius in Elliptic Orbit*Perigee Radius in Elliptic Orbit)

Semimajor Axis of Elliptic Orbit given Apogee and Perigee Radii

Go Semi Major Axis of Elliptic Orbit = (Apogee Radius in Elliptic Orbit+Perigee Radius in Elliptic Orbit)/2

Angular Momentum in Elliptic Orbit Given Perigee Radius and Perigee Velocity

Go Angular Momentum of Elliptic Orbit = Perigee Radius in Elliptic Orbit*Velocity of Satellite at Perigee

Radial Velocity in Elliptic Orbit given Radial Position and Angular Momentum

Go Radial Velocity of Satellite = Angular Momentum of Elliptic Orbit/Radial Position in Elliptical Orbit

Angular Momentum in Elliptic Orbit Given Apogee Radius and Apogee Velocity

Go Angular Momentum of Elliptic Orbit = Apogee Radius in Elliptic Orbit*Velocity of Satellite at Apogee

Apogee Velocity in Elliptic Orbit Given Angular Momentum and Apogee Radius

Go Velocity of Satellite at Apogee = Angular Momentum of Elliptic Orbit/Apogee Radius in Elliptic Orbit

Eccentricity of Orbit

Go Eccentricity of Elliptical Orbit = Distance Between Two Foci/(2*Semi Major Axis of Elliptic Orbit)

Specific Energy of Elliptic Orbit given Semi Major Axis

Go Specific Energy of Elliptical Orbit = -[GM.Earth]/(2*Semi Major Axis of Elliptic Orbit)

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum Formula

Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit
v_r = [GM.Earth]*e_e*sin(θ_e)/h_e

Kepler's Laws and Gravitational Attraction

Johannes Kepler's laws of planetary motion, developed in the 17th century, provided significant insights into the relationship between celestial bodies and gravity. Kepler's laws describe the elliptical orbits of planets and other objects in the solar system, all of which are governed by the gravitational pull of the central body, such as the Sun. These laws laid the foundation for understanding how gravity affects the motion of objects in space, paving the way for Sir Isaac Newton's formulation of the law of universal gravitation.

How to Calculate Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum?

Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum calculator uses Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit to calculate the Radial Velocity of Satellite, The Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum formula is defined as component of velocity directed along the line connecting the object to the central body. This formula allows for the calculation of radial velocity based on three critical parameters: true anomaly, eccentricity, and angular momentum. Radial Velocity of Satellite is denoted by v_r symbol.

How to calculate Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum using this online calculator? To use this online calculator for Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum, enter Eccentricity of Elliptical Orbit (e_e), True Anomaly in Elliptical Orbit (θ_e) & Angular Momentum of Elliptic Orbit (h_e) and hit the calculate button. Here is how the Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum calculation can be explained with given input values -> 0.002567 = [GM.Earth]*0.6*sin(2.3581143523691)/65750000000.

FAQ

What is Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum?

The Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum formula is defined as component of velocity directed along the line connecting the object to the central body. This formula allows for the calculation of radial velocity based on three critical parameters: true anomaly, eccentricity, and angular momentum and is represented as v_r = [GM.Earth]*e_e*sin(θ_e)/h_e or Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit. Eccentricity of Elliptical Orbit is a measure of how stretched or elongated the orbit's shape is, True Anomaly in Elliptical Orbit measures the angle between the object's current position and the perigee (the point of closest approach to the central body) when viewed from the focus of the orbit & Angular Momentum of Elliptic 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.

How to calculate Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum?

The Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum formula is defined as component of velocity directed along the line connecting the object to the central body. This formula allows for the calculation of radial velocity based on three critical parameters: true anomaly, eccentricity, and angular momentum is calculated using Radial Velocity of Satellite = [GM.Earth]*Eccentricity of Elliptical Orbit*sin(True Anomaly in Elliptical Orbit)/Angular Momentum of Elliptic Orbit. To calculate Radial Velocity in Elliptic Orbit given True Anomaly, Eccentricity, and Angular Momentum, you need Eccentricity of Elliptical Orbit (e_e), True Anomaly in Elliptical Orbit (θ_e) & Angular Momentum of Elliptic Orbit (h_e). With our tool, you need to enter the respective value for Eccentricity of Elliptical Orbit, True Anomaly in Elliptical Orbit & Angular Momentum 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 Radial Velocity of Satellite?

In this formula, Radial Velocity of Satellite uses Eccentricity of Elliptical Orbit, True Anomaly in Elliptical Orbit & Angular Momentum of Elliptic Orbit. We can use 1 other way(s) to calculate the same, which is/are as follows -

Radial Velocity of Satellite = Angular Momentum of Elliptic Orbit/Radial Position in Elliptical Orbit

Home

FREE PDFs

🔍 Search