# Questions tagged [orbital-mechanics]

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. For the movements of celestial bodies, see [celestial-mechanics].

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### Delta-V chart mathematics

Could someone explain me the mathematics behind the Delta-V charts one can find on internet such as:                 &...
14k views

### Is there a lot of space trash at the Earth-Moon Lagrange points?

Lagrange points are the points in a multi-body gravitational system in which the gravitational force and centrifugal force sum to zero. The image below from this Wikipedia article shows the 5 ...
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### What is the optimal inclination change strategy?

Consider a transfer between two circular orbits of similar radius, the only difference being the inclination difference, $\alpha$. What's the minimal $\Delta v$ required to perform this transfer? ...
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### How to calculate the time to apoapsis & periapsis, given the orbital elements?

I have the 6 orbital elements (excluding Time of Periapsis Passage, obviously), 2 state vectors, and a lot of other parameters like orbital period. I am looking to use them to calculate the time to ...
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### Why should the James Webb Space telescope stay in the unstable L2?

We all know that James Webb Space telescope is planned to be launched in 2018. It has been decided that the orbit of JWST will be elliptical around the Lagrange point L2, which has been declared as ...
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### How large is the Earth's gravitational Sphere of Influence and how can it be calculated?

There was a recent update on ISRO's Mars Orbiter Mission's (MOM) Facebook page that it has crossed the Earth's Sphere of Influence (SOI): MOM moves on! MOM is going to cruise out of the sphere ...
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### Was the Apollo spacecraft always gravitationally bound to the Earth-Moon system?

When the Apollo spacecraft was en route to the Moon, was it an escape trajectory from the Earth-Moon system? If not for the burn(s) to enter lunar orbit, would it have continued in an independent ...
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### Where is the optimal location to launch payloads to outer space?

Imaginary scenario: The US, Russia, China, Europe, India, and all the private space companies in between combine resources for a sustained space exploration program beyond Earth. They can choose any ...
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### How would we move Venus or Mars into Earth's orbital zone? [closed]

(See the more focused version of this question: How long would it take to move Venus and Mars into Earth's orbital zone using gravity assist?) What methods and time scales might be involved in moving ...
29k views

### Calculating solar system escape and and sun-dive delta V from lower Earth orbit

According to http://en.wikipedia.org/wiki/Escape_velocity at the Earth/Moon distance from the sun, the escape velocity is 42.1 km/s. According to http://en.wikipedia.org/wiki/Earth the average ...
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### How frequently do asteroids collide with each other?

Space is empty ... lots of empty. Apparently so empty that the risk of collision between a spacecraft of our times, and an asteroid in the asteroid belt is said to be infinitesimal. Running a search ...
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### What does the BackFlip lunar cycler do in its pass by Earth?

This paper describes an Earth-moon cycler orbit. In this concept, a 180 degree "BackFlip" is used to modify a more simple cycler orbit. However, I can't figure out what cycler orbit it modifies, and ...
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### How to calculate apoapsis of sub-orbital trajectory?

I have made a RK4 simulator for launching a cannonball from a tower. Which has the state variables: Position vector r Velocity vector v Mass of planet M To simplify it, working in only 2 dimensions (...
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### ECI to LVLH conversion

I want to transform the position and velocity of two satellites from ECI mean of date mean of equinox to LVLH(Local Vertical Local Horizontal). The problem is that there is little documentation that I ...
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### Has a TLE ever been issued for a spacecraft trajectory not bound to Earth orbit?

This excellent answer to the question Why has no TLE been published for the DSCOVR satellite and the Falcon 9 R/B? suggests that to the best of the writer's knowledge TLEs are only issued for ...
868 views

### Spacecraft Maneuvers as Intellectual Property? Wow!

In the past I had encountered a few mentions of orbits being patented (or at least applications filed) but didn't take much notice. Then I did a simple search and was blown away by the sheer volume of ...
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### Apollo 10: Where's Snoopy?

During the Apollo program, we launched a total of 9 Lunar Modules (LM's). The Ascent module from Apollo 10, or "Snoopy," is unique in that it was neither deliberately crashed into the Moon (Apollo 11, ...
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### 2nd stage speed - with respect to what? (SpaceX webcast of Orbcomm OG2 deployment)

As a follow-up question to this answer by @TildalWave, exactly what frame is used to calculate the "speed" in the inset display of speed and altitude in the SpaceX broadcast of the Falcon 9 launch and ...
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### What force is bringing Cassini down into Saturn's atmosphere in another 145 days; drag, or…?

Headlines suggest (as do their articles) that as a gravitational result of Cassini's final flyby of Titan, it's fate is sealed and it's orbit is destined to take it into Saturn's atmosphere on ...
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### What's the eccentricity of an orbit (trajectory) falling straight down towards the center?

Discussion below this answer has got me thinking. A circular orbit has eccentricity of $\epsilon = 0$, ellipses $0 < \epsilon < 1$ (between but not including 0 and 1), and parabolic and ...
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### Why is Nodal precession affected by the rotational period of the planet?

The $J_2$ term in Nodal Precession equation has the rotational period of the planet. I understand that the oblateness of the sphere with an equatorial bulge induces a torque on the orbit of a ...
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### How was the radius of Venus measured so accurately (± 3 km) via radar in the mid 1960's, before Venera 4 and Mariner 5?

In several answers to the question When did planetary scientists realize Venus' surface pressure was almost 100x that on Earth? How did they find out? the known radius of Venus is mentioned. It was ...
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### Nature of Hayabusa-2's “Home Position” relative to Ryugu? Is it Ruygu's L1?

This tweet "from Hayabusa-2" via JAXA shows the diagram below, which seems to suggest that the Hayabusa-2 spacecraft tends to remain between the asteroid Ryugu and the Sun. Does Hayabusa-2 have to ...
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### Will the new “TLE format” be orbitally-mechanically better than traditional TLEs?

Celetrak's A New Way to Obtain GP Data (aka TLEs) by Dr. T.S. Kelso 2020 May 27 explains the arrival a new infoblob format that in several ways is "better" than the ancient TLE, and contains ...
381 views

### Need help getting the true ICRF coordinates of SOHO using Horizons

In this answer I calculated the approximate angular separation between Mercury and the Sun as seen by the SOHO satellite using Skyfield's method of ...
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### How to get lunar L, B, C parameters from the Moon's 3x3 rotation matrix from the Python package Skyfield?

Answers to What are the “Moon L, B, C” angles shown in this solar eclipse simulation? explain that L and B (or "l" and "b") are the "selenographic coordinates of the Moon's apparent center" (latitude ...
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### What (actually) is a 1:1 resonance, and is 2016 HO3 in one with the Earth?

In my question How was Earth's "quasi-satellite" 2016 HO3 "first spotted" and it's orbit determined? I link to two videos of simulations of views of 2016 HO3's orbit seen in two ...
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### Time dilation between Mars and Earth due to different mass

I am not sure I understand the Time dilation correctly but if mass has dirrect impact on time...than lets consider cosmological event - one orbit of planet Earth around Sun. This event will person on ...
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### How to correctly make a fake, counter-propagating TLE?

In this answer I have said: Do not make FAKE TLEs! I would now like to make a fake TLE. Specifically I'd like to generate a counter-propagating "twin" of an orbit by flipping inclination by 180° ...
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### How to get velocity vector from GPS NMEA data?

I am writing a program to receive and interpret NMEA data from a GPS receiver. I am working with an Adafruit Ultimate GPS Receiver integrated with an Arduino. The \$GPRMC NMEA Sentence contains the ...
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### Why does Earth not appear to be at the focus of TESS' elliptical orbit in this video?

An excellent review of all of the considerations and work that has gone into designing TESS' orbit can be read in the ArXiv preprint A High Earth, Lunar Resonant Orbit for Lower Cost Space Science ...
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### Rendezvouses in halo or lissajous orbits

If a spacecraft was in an EM-L2 halo/lissajous orbit, and another craft would was going to approach EM-L2 a few days later, could they rendezvous immediately or is there a limitation when the second ...
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### What's the method behind this TDRS triplet inclination “madness”?

Previous "method to the maddness" questions: 1, 2. The image below is from Why does TDRS 1's inclination evolve so much differently than that of all the others starting in 1995? and I've used it a ...
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### Is the Flyby Anomaly still a thing?

The Flyby Anomaly is a name given to an unexplained, unexpected difference between the best theoretical calculation of a change in several different spacecraft's velocities due to flyby (Gravity ...
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### How does the ISS Transit Finder website get the position of the ISS so accurately?

The recent Petapixel article How to Shoot the ISS Flying Across the Face of the Moon gives a lot of detailed, helpful advice for photographing transits of the ISS across the disk of the Moon. For ...
573 views

### What was the first practical use of a satellite constellation?

If I loosely define "constellation" here as a group of earth satellites where different ones are visible at different times, and you need all or most of them to get round-the-clock coverage, some ...
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### What are the “Moon L, B, C” angles shown in this solar eclipse simulation?

The NASA Goddard video Tracing the 2017 Solar Eclipse is a visualization of the calculated shape of the umbra during the upcoming August 2017 total solar eclipse, as it moves across North America. The ...
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### I've almost learned to spell Chebyshev, why has JPL switched to Hermite interpolation for DE438?

According to @ChrisR's thorough answer One caveat however is that the interpolation in DE438 is a Hermite interpolation, and no longer a Chebychev interpolation, so you may need to update your code....
196 views

### How much does the tidal effect affect satellites in a retrograde orbit?

How much more unstable are satellites in retrograde then a pro-grade orbit? Does the stability of a retrograde orbit increase with altitude? This answer said this orbit is unstable and made me think,...
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### For constellations of circular LEO satellites, are there allocations of available “slots” in altitudes?

The BBC article SpaceX aims to launch internet from space discusses the SpaceX proposal for a dense array of 4,425 LEO satellites distributed among 83 orbital planes in five inclination groups as ...
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### Where is Lucy going? (asteroid mission)

On Halloween (31-Oct-2018) NASA Goddard announced that Lucy has a green light: NASA’s Mission to Jupiter’s Trojans Given the Green Light for Development All I have are these links which are now ...
468 views

### Will the Tesla Roadster/Falcon 9H 2nd stage ever be a navigation hazard to cis-lunar space?

The saying "What goes around, comes around" can apply to spacecraft on ballistic trajectories that are launched from Earth into bound heliocentric orbits. Since the Tesla Roadster/Falcon 9H 2nd stage'...
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### Will the Emirate Mars Mission, Tianwen-1 and Mars 2020 Mission get closer to each other or spread out on their way to Mars?

Background & Introduction: On August 2, 2020 the brand new Where Is Roadster page Spacecraft launched to Mars in 2020 (announced here) said that it had been: 13 days, 3 hours, 47 minutes and 13 ...
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### Did SpaceX intend to overshoot Mars?

There seems to be a lot of buzz around the Internet that the now famous Roadster is going to overshoot mars. Was this intentional, just to show the kind of capacity it is capable of? Or was there some ...
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### How does the “eccentricity-inclination vector separation” technique work for colocated GEO satellites?

This answer to How are co-located satellites positioned relative to each other? links to the paywalled paper Separation of Geostationary Satellites with Eccentricity and Inclination Vector with the ...
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### Design of an elliptical transfer orbit

I was working an example in Charles Brown's "Elements of Spacecraft Design" but I can not figure out how the Time of Flight was calculated. Here is the problem Example 6.5. I got the correct answer ...
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### Orbital vocabulary confusion! How can the tangential velocity of an elliptical Kepler orbit not be tangent to the orbit?

I'm now officially confused about the usage of "tangential" when breaking down orbital velocity components. It started with edits and comments on this answer to Orbital speed is (vector) sum of ...
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### Roughly how many kinds of closed or periodic orbits are there in the circular restricted three-body problem?

Question: Roughly how many kinds of closed or periodic orbits are there in the circular restricted three-body problem? Has anyone made an attempt to enumerate and classify/categorize them? Notes: If ...
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### What is a “synodic frame”? Can one be defined for an elliptical orbit?

A description of a "synodic frame" was one of the main ingredients in this excellent answer to a question about an animation of a funky-looking orbit that several different and distinctly interesting ...
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### Why can't custom-made TLEs for the DSCOVR launch booster in orbit around Earth work with SDP4?

This fascinating answer to Why has no TLE been published for the DSCOVR satellite and the Falcon 9 R/B? presents links to custom-made TLEs for the Falcon 9 rocket body that put DSCOVR into orbit, and ...