What is Orbital mechanics: Definition and 87 Discussions

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control.
Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers.
General relativity is a more exact theory than Newton's laws for calculating orbits, and is sometimes necessary for greater accuracy or in high-gravity situations (e.g. orbits near the Sun).

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  1. J

    I Plotting the orbits of the planets from Ephemeris data

    I would like to plot the position of planets around the Sun for different dates and describe their orbits. I got the Ephemeris data for each planet from the JPL Horizons System, I got: Date__(UT)__HR:MN R.A.___(ICRF)___DEC Ang-diam ObsSub-LON ObsSub-LAT ObsEcLon ObsEcLat however...
  2. S

    I Tidal effects of galaxies orbiting one another with dark energy?

    I recently found a question in a physics discussion site [1] about whether there was a "distance" between two galaxies where both the gravitational force and the influence of dark energy would be balanced. The answers and comments seem to indicate that there is indeed such a "radius" around a...
  3. S

    I Would there be any way to avoid gravitational wave emissions?

    In principle every object orbiting another (e.g. a planet revolving around a star) would emit gravitational waves, relaxing the orbit over time.However, this would not happen if the orbits had a time-invariant and symmetric quadrupole moment. As it is indicated in this question (), it appears...
  4. S

    B Homopolar motor rotation in Vacuum

    Hi again, I've found interesting video. Roller homopolar motor : Roller Motor Do you think the motor from 1:08 min Will self rotate in Vacuum/Space (No other forces : Gravitational or Other type.) Thank you in advance.
  5. N

    I Orbital Precession Calculation: Unit Explained

    Hi, I've just calculated the orbital precession for the earth using the sigma formula of general relativity. $$ \sigma=\frac{24 \pi^{3} R^{2}}{T^{2} c^{2}\left(1-e^{2}\right)}=\frac{24\pi^3×1.5×10^{11}}{3×10^7×3×10^8(1-0.0034^2)}=0.012 $$ What is the unit of the result? Degrees per century or...
  6. D

    I Can a Satellite Maintain its Angular Velocity with Continuous Low Thrust?

    Suppose two satellites are in a circular heliocentric orbit with radius R and with angular velocity O'. Satellite 2 then undergoes a low continuous thrust. Can Satellite 2 (the one that undergoes the continuous low thrust) maintain the same angular velocity O' about the sun? It seems that...
  7. C

    Numerical Methods for Learning Orbital Mechanics

    I'm interested in learning orbital mechanics but I haven't taken a class in numerical methods yet. Do I really need to take a whole class in numerical methods before learning orbital mechanics, or can I get by if I self-learn a smaller portion of the syllabus of a numerical methods class? If so...
  8. adammish

    What is the relationship between tension and mass for an artificial satellite?

    Hi, I need to prove that the tension for artificial satellite consists of two points of mass m/2 connected by a light rigid rod of length , the tension in the rod is - $$ T=\frac{3}{4}\frac{Gmm'l}{a^3}-\frac{1}{4}\frac{Gm^2}{l^2} $$ the satellite is placed in a circular orbit of radius a>>l...
  9. D

    B Observing Orbital Mechanics from the 2nd Focus of Earth's Orbit

    If a hypothetical spacecraft could keep station at the 2nd focus of Earth's orbit, what useful observations could be made? Each minute sees a new solar triangle Earth Sun Craft (ESC). Swept area remains constant, as should length SC, and length CE + ES. With the Sun as our point source...
  10. J

    Orbital mechanics: is ballistic capture possible without acceleration?

    All spacecraft that have been put into orbit around other planets have required engines to decelerate them and inject them into their orbits. So-called "ballistic capture", from what I've read, always seems to call for at least a minimum application of force to change the trajectory; I get...
  11. SJay16

    How would one estimate the rotation period of a star from its spectrum

    The figure is shown; the measurements were taken on two consecutive observing nights. The Ordinate is the flux normalized to continuum and the abscissa is the wavelength scale. You can see the "bumps" indicated by the arrows referring to some Starspot as the spot moves on the profile; assuming a...
  12. S

    MATLAB How can I plot a Hohmann Transfer Orbit in MATLAB using ode45?

    function Asteroid_Mining clc %Initial conditions g0 = 9.81; %gravity (m/s^2) p = 1.225; %atmospheric density at sea level (kg/m3) Re = 6378; %radius of Earth (km) Ra = 7.431e7; %distance of Bennu from Earth in (km) [August 2023] G = 6.674e-11/1e9; % Gravitational constant (km3/kg.s2) mu =...
  13. S

    MATLAB Calculating the time taken for an asteroid mission using MATLAB

    Using MATLAB, I am trying to calculate the time taken for a spacecraft to travel from Earth to a near Earth asteroid and then returning back to Earth but so far I have had no luck. Furthermore, I want to plot a Hohmann transfer and calculate the mass of fuel required for this mission. If...
  14. cybernetichero

    Orbital mechanics question about Star Trek

    I'm watching the Next Generation episode Relics and Riker has just ordered the helm to "go into orbit above that point" which I took to mean geosynchronous orbit. No biggie except that the point is on the outer surface of a Dyson Sphere with a RADIUS of more than 1AU. So, assuming the sphere has...
  15. Andres Padilla

    Problem about orbital mechanics

    I tried it, but I am not getting no of the given answers According to the statement, it is saying that 3 KE (in the orbit ) = ΔUg So, beeing R the radius of the Earth and R2 the radius of the orbit: 3 (1/2)(GMm/r2) = -GMm/r2 - (-GMm/R) Canceling out the GMm: (3/2)(1/r2)= (-1/r2) + (1/R)...
  16. Q

    Orbital Slingshot and Conservation of Momentum Confusion

    Hello, I am an undergrad and am in an introductory level astrophysics course. I have a bit of confusion that I didn't know where to get help from so I made an account here. Please let me know if I miss some common etiquette or something... I don't understand how the slingshot maneuver...
  17. A

    I Black hole orbital mechanics questions

    What are some of the challenges associated with calculating orbital parameters of objects around a black hole (I.e. Orbital velocity, period, semi major axis, kinetic energy). At what point can classical physics no longer provide accurate results?
  18. J

    Gravitation & Orbital Mechanics: Is One Method More Correct Than the Other?

    I have been going through problems in my textbook and have a question. The chapter is on gravitation and orbital mechanics. When answering the problems I seem to head towards different methods than what the book prescribes. My answers, primarily using known orbital equations, are close, but not...
  19. Russell Patterson

    Insights Orbital Mechanics in Unity Game Engine for Augmented Reality - Comments

    Greg Bernhardt submitted a new PF Insights post Orbital Mechanics in Unity Game Engine for Augmented Reality Continue reading the Original PF Insights Post.
  20. L

    Maple Computational Hohmann Transfer on MapleSoft

    Hi, I am trying to recreate an Interplanetary Hohmann transfer orbit from Earth to Mars similar to image A below (the red line). However, Earths orbit is not circular, It is more of an elliptical orbit rather than circular. I was able to successfully plot the orbits of both Earth and Mars...
  21. FQVBSina

    Orbital Mechanics Angular Momentum

    Hello all, I have a question regarding the precise definition of angular momentum in orbital motion. I see one definition says angular momentum h, position, r, and radial velocity, r_dot, are related as follows: h = r x r_dot. However, I also see one definition that says h is related to r and...
  22. FQVBSina

    Orbital Mechanics Vis Viva Equation Question

    In the case of a satellite orbiting the Earth. Would the relative velocity calculated by the Vis Viva equation the same as the orbital speed of the satellite? If the satellite is in an ellipse, would Vis Viva give the circular tangential velocity Vt=rω, or would it give the orbital velocity...
  23. PlanetGazer8350

    Calculate iron container acceleration in railgun system on the Moon

    Having a cylindrical iron container with wall thickness of 20 cm, and a total weight of 500 tons when filled with its cargo, how would you be able to calculate its required voltage and current input in a vertical railgun system (relative to the Moon's surface), with an exit acceleration of...
  24. M

    I Orbit simulations, tidal forces and planetary oblateness

    How does one correct for tidal forces when (classically) simulating the orbits of solar system bodies?
  25. A

    Points on an elliptical orbit where V(radia) is zero.

    Homework Statement Points on an elliptical orbit where the speed is equal to that on a circular orbit? Homework EquationsThe Attempt at a Solution I have attempted this question and my calculations show that at points on minor and major axes, the radial component of velocity is zero. Hence at...
  26. P

    I The Sun's habitable zone and orbital resonaces/stability

    Let's say there's five Mars/Earth massed planets orbiting a star like the sun between 0.6 AU and 2 AU, what orbital resonance configuration can they be into ensure maximum stability? Would adding gas giants to the system enhance stability?
  27. JayFlynn

    Why use Earth as a gravity assist?

    I am doing research for my aerospace engineering dissertation to plan a mission to a Jupiter trojan asteroid. I was researching the type of outgoing trajectories used in missions such as JUNO, Galileo and Europa and noticed they all use Earth as a gravity assist in getting to deep space. Surely...
  28. J

    A Series of Exoplanets in Our Solar System

    In this alternate universe, Earth is the same as back home--8,000 miles wide, 25,000 around, six sextillion tons, orbiting a G-type main-sequence star from a distance of 93 million miles. But here, the similarities end. MOON DIAMETER--3,273 miles MASS--0.025x that of Earth DISTANCE FROM...
  29. J

    Writing: Input Wanted Eleven Inner Planets--What Will Earth's Ice Ages Be Like?

    A Milankovitch cycle is defined in Universe Today as "a cyclical movement related to the Earth’s orbit around the Sun." There are three elements to a Milankovitch cycle that affects the amount of solar heat and with it, the Earth's climate: Eccentricity (Orbital Shape)--The elliptical shape...
  30. A

    I Plotting the orbits of the planets

    Hello everybody! Long-time lurker and second-time posting. I'm working on a project for my math class, and I'm trying to plot the orbits of the planets using vectors. I've chosen to use MATLAB because I am decently familiar with it. I've used the formulas described in this post here to get my...
  31. P

    B Orbital Mechanics: GR vs Newton's Laws

    9/1/2016 Orbital mechanics Wikipedia, the free encyclopedia This reference states: "General relativity is a more exact theory than Newton's laws for calculating orbits, and is sometimes necessary for greater accuracy or in highgravity situations (such as orbits close to the Sun)". Can GR...
  32. Phys_Boi

    Orbital Mechanics: Modeling a Planet's Path with Programming

    So I'm really interested in orbital mechanics. I'm only 16 so my knowledge of physics is restricted to an intermediate level. If there is a planet with large mass and a planet with small mass they are attracted to each other... So imagine a system where the large mass is fixed and the small...
  33. Philip Robotic

    B Welcome to Physics Forums: Exploring Orbital Mechanics & Gravity

    Hi everyone! I'm really sorry if I'm using the wrong forum. It's my first time at PF. I'm pretty new to physics, as I began studying it just two years ago, but I'm really interested in the subject of astrophysics so I bought myself and started reading 'Introduction to rocket science and...
  34. A

    I Seeking "simple" orbital path planning for game development

    Hi PhysicsForums! I'm a game developer planning a project involving simplified, idealized orbital mechanics. I made this reddit post which did not generate the sort of response I was hoping for, but it summarizes my issue in greater detail for anyone curious...
  35. Stollaxel Stoll

    B What exactly is L, Lz and E in orbital mechanics?

    I often stumbled across the variables for angular momentum L and axial angular momentum Lz, which would be no problem if working in cartesian coordinates, then it would be Lz = px y - py x. Unfortunately I have no idea what to make of an Lz in spherical coordinates: For example, in equations of...
  36. P

    Geostationary satellite orbit radius as a multiple of Earth radius.

    Homework Statement Okay, so the question seems really simple so I don't know what I'm missing A satellite orbits at a fixed point above the Earth's equator. Assuming the Earth has uniform density, radius R, and angular frequency of rotation, omega Find an expression for eta, such that the...
  37. T

    Equations associated with calculating velocity of a bullet.

    Hello, I'm currently doing a project on a Verne gun, and I'd just like to know which equations I should know in order to explain such a device. How do i calculate velocity, efficiency of the launch, how the gas laws play into the efficiency, since it should be traveling at 10s of kilometers a...
  38. R

    Time dilation magnitude in orbit around a black hole

    Hello, I'm working on a hypothetical situation involving a planetary body orbiting a black hole (similar to the scenario in Interstellar, but for different reasons), trying to balance tidal forces with orbital distance and time dilation. First, I'm interested in the effect of gravitational...
  39. sevenperforce

    Suborbital docking - Apollo Landings

    Suppose that one of the Apollo landings had developed a fuel leak in the lunar ascent module, such that even with a lightened load, the ascent module only had enough delta-v to reach about half of lunar orbital velocity. One possible rescue solution would be to lower the command module's orbit...
  40. J

    [Orbital mechanics] Asteroid angular momentum

    Homework Statement : [/B] A vector is perpendicular to B vector, and they stay still, relative to the body. No torque is applied on the asteroid, although he dissipates very little rotational kinetic energy, due to drag on dust clouds. It was also determined that the asteroid is a long body...
  41. xpell

    How (un)stable are the Lagrangian points 1, 2 and 3?

    A couple questions, please: I know that the Lagrangian points 1, 2 and 3 are unstable and special Lissajous orbits plus some station-keeping are required to place a spacecraft around them. But I was wondering if they are so totally unstable that they can't temporarily "capture" a passing...
  42. P

    Solve Orbital Mechanics Problems: Calculate Satellite Energy

    I'm having trouble with orbItal mechanics, I'm trying to determine the total potential energy of an orbiting satellite, what I've done so far is this: I know m*g*h is potential energy, but I also know that gravity deceases with distance avoiding to the inverse square law. I know I Just can't use...
  43. T

    Runge-Kutta method - Orbital mechanics

    Homework Statement Given: Initial orbital elements of a satellite a=6652.555663km; e=0.075; i=28.5 degrees; Ω=40 degrees; w=30 degrees; n=0 degrees;Tasks(using MATLAB): 1. Convert orbital elements to position and velocity vectors 2. Use these vectors to initialize the Runge-Kutta...
  44. xpell

    Heliocentric polar orbit crossing the Earth's orbit twice

    Sorry, the title's length didn't allow me to explain this better and I need it for a story that I'm writing, if you're so kind to help me. I've been trying it hard to solve it myself but I've been unable to. The problem looks simple but it isn't (for me): Please assume we have a space probe of...
  45. KenJackson

    Calculating relativistic effects of motion in solar system

    This question and answer are posed in Kim Stanley Robinson's novel "2312". My question is, is this all made up? Or might it be accurate?
  46. T

    Is Tidal Circularisation of Orbits a Tricky Concept?

    Homework Statement A body on an orbit with semi-major axis a and eccentricity e undergoes tidal circularisation. Show that the orbit will circularise at a semi-major axis, acirc, given by acirc = 2rperi = 2a (1 − e). Homework Equations No equations given, but I think the following could...
  47. P

    Orbital Rendezvous and Mission Control Involvement

    Can someone please give a step by step explanation of an orbital rendezvous by a spacecraft for a target that is orbiting the body it launched from? And if possible, can you explain how mission control is involved and what part computers play? When the RCS is active is it changing the...
  48. T

    Orbital Mechanics: Find Eqns of Motion w/ Initial Conditions

    Hello, After searching on the internet, I have come to the conclusion that there is no completely general way to calculate the position of an orbiting body. My question is whether there is a way to find the equations of motion with respect to time of a satellite orbit given only the initial...
  49. P

    What is the relationship between orbital semi latus rectum and angular momentum?

    Hi. I have recently been trying my hands at calculating a few orbits but have encountered difficulties in trying to 'understand' the semi latus rectum. P=h^2/GM What does it have to do with the orbiting object's angular momentum? How come I get different values when I derive it from other...
  50. T

    In depth Mars flight trajectory studies

    Can anyone point me in the direction of any published scientific work involving the study of Earth to Mars flight trajectories? I am thinking of researching this topic for a project and I would like to know about the work that has already been done.
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