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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Does it take the same amount of energy to get to Mars vs. to rendezvous with something going to Mars?

I think I found a mathematical error in the 2015 movie The Martian1. Warning, there will be spoilers. The final plan they settle on to rescue Mark Watney is to have the Tiayang Shen rendezvous with ...
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what range of orbital inclinations will be needed to reach Mars from the Boca Chica launch site?

When SpaceX fly missions out of Boca Chica in South Texas to Mars what orbital inclination will the launch need to be to put the spacecraft on to best transfer orbit to Mars? And will this vary with ...
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How to calculate the velocity vector in the case of a hyperbolic orbit?

The problem I'm trying to get a formula to calculate the state vectors $\vec{r}$ and $\vec{v} = \dot{\vec{r}}$ on an orbit, given a true anomaly $\nu$. I'm following the process described here : https:...
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How to calculate the time to reach a given true anomaly? [closed]

I'm looking for a general formula or procedure calculate time to reach any given true anomaly.
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Are the initial conditions for the Apollo PFS objects' orbits known (or knowable) as well as they were for the ascent module?

This answer to Would we have spotted the ascent stage of Apollo 11's Eagle if it was still in orbit around the Moon? and discussion under it suggests that as a check of the orbital propagation ...
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How to generate TLEs based on a set of observation points (location, azimuth, elevation… no range)

I'm interested in generating a "corrected TLE1" based on observation data. I would have observed azimuth and elevation, site location, and time. All of those data fields are observed with ...
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1answer
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Finding the new true anomaly after performing a maneuver

Given a standard set of orbital elements (angular momentum, semi-major axis, eccentricity, inclination, longitude of the ascending node, argument of periapsis, and true anomaly), and a global time ...
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What is the shape of the envelope of all orbits with velocity of equal magnitude at their intersection?

Also known as: where can I go with my delta-v budget? For parabolic trajectories in uniform gravity, the answer is a parabola. Thats why I'm surprised that the same envelope for elliptical orbits ...
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Why does higher solar phase angle (SPA) allow for many more feasible FastKD (kinetic deflection) communications satellite “hijacking” missions?

Space.com's advert-laden Repurposed communications satellites could help save humanity from an asteroid impact ends with: The study results were presented at the Planetary Defence (sic) Conference ...
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References for constant low-thrust spiral up-coast-spiral down phasing maneuvers for circular and non-circular orbits?

I am trying to find papers that describe constant low-thrust spiral up-coast-spiral down phasing maneuvers for circular and non-circular orbits. The thrust is assumed to be fixed at $T_{const}$ when ...
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What are the energy requirements to reach Earth orbit and Mars orbit assuming no efficiency losses?

Suppose some magic propulsion method exists which directly converts electricity into kinetic energy. And its efficiency is 100%. And its weight is 0. What is a way to calculate the energy requirements ...
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Puzzler; what can we learn about the distance and direction of Earth from this cool SpaceX-tweeted image of Earth and a vacuum nozzle?

The 18-June-2021 Spacex-tweeted below says: View from Falcon 9's second stage Merlin Vacuum engine There is information out there about the approximate exit diameter and length of the nozzle and ...
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What asteroids have the least delta-v to reach?

I think the question needs very little clarification - specific asteroids and/or their asteroid orbit type would answer it. My own interest is in what would best suit targeting for asteroid mining on ...
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1answer
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Rotation matrix / coordinate transformation of maneuver parameters from Prograde, Normal, Radial to Cartesian XYZ?

Say I have a state vector and Keplerian elements of an orbiting spacecraft: Position = [x, y, z] Velocity = [vx, vy, vz] Elements = [a, e, i, $\omega$, $\Omega$, $\nu$] And I have the maneuver I ...
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Is it possible for the exhaust plume of a rocket engine burning retrograde to accelerate an object into an even higher orbit?

A couple weeks back, a debris object was catalogued in a 210x540km orbit following the deorbit burn of the Falcon 9 second stage that launched CRS-22: Hmm... possible that CRS-22's stage 2 made ...
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1answer
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Do geodesics close on an ellipsoid?

I want to calculate the shortest distance between two points (Point A and Point B) on the ellipsoid surface. For this I need to use geodetic passing through these two points. Well, if I continue this ...
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Would knocking the moon off it’s tidal lock with Earth affect its orbit?

Lots of discussion about terraforming the moon involves smacking it with a comet such that it rotates with a 24 hour ish period. But I don’t know if this will affect its orbit in any way. Is it ...
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What orbits are Starlink satellites now deployed into? How low to do they go on their first perigee?

In my answer to Delta-V of Starlink Satellites I ballpark spherical-cow envelope-back estimated 190 m/s with 2 kg of krypton based on raising only from a 445 km circular orbit to a 550 km circular ...
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Textbook or scholarly discussion of equations used by the SDP4 part of SGP4 TLE propagators beyond Space Track Report #1?

(the famous) Space Tract Report #3 discussed at length in Dr. T.S. Kelso's Revisiting Spacetrack Report #3, AIAA 2006-6753 Describes the "deep space" corrections to the original SGP4 known ...
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In a 3D space defined by semimajor axis, eccentricity and inclination, what would be the shape of the space where SDP4 works better than SGP4?

@BillGray's answer to Why can't custom-made TLEs for the DSCOVR launch booster in orbit around Earth work with SDP4? is quite interesting and informative; I fail to do it justice by summarizing it as ...
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Is the formula for nodal period of a near-Earth satellite given by Wikipedia correct?

Wikipedia has a formula for the nodal period of a near-Earth satellite, taking into account the oblateness of the Earth (J2), and neglecting other effects (https://en.wikipedia.org/wiki/Nodal_period)....
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Time to reach interstellar space

From my understanding, both voyager 1 and voyager 2 used a gravity assisted slingshot method to leave the solar system. Question(s): Since the planetary alignment used won't happen again for a while, ...
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How to find a vector's elevation angle with respect to a point on Earth?

tl;dr: Spacecraft's antenna should point to a ground station but there is a pointing error. I want to express the error as a vector rather than a simple angle that a dot product provides, so that I ...
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Source of Satellite and Debris Ephemerides for Analysis

I'm working on some code that will fuse ephemeris data, the raw telescope and radar data used for locating and tracking active satellites and space debris. Most of this data is owned by the Air Force ...
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How can we mine Near Earth Objects?

After skimming this Worldbuilding SE answer, I wonder if any companies or space agencies have plans in place to mine Near Earth Objects(NEOs) in the future.
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Just how much “dumb luck” was reaching the space age during the “Grand Tour” opportunity? Would we have been SOL 1050 or 2100 years before/after?

@OscarLanzi's answer to Why is the gas giant grand tour interval 175 years when the synodic period of Uranus and Neptune is 171 years? is an excellent answer describing a subtle situation; each pair ...
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Calculating body frame X vector's look direction in GEO (NED) frame from roll, pitch and yaw data, is this correct?

I have roll, pitch and yaw angle values for a LEO satellite. Satellite orbit frame and spacecraft body frame are defined as LVLH. The satellite position and velocity are given in ECI/GEI frame. I have ...
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1answer
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How can I calculate the future position of a satellite orbiting a central body as a function of time using known orbital elements?

Given the position and velocity vectors at one point in an orbit, one can calculate the keplerian elements and thus graph the subsequent orbital path as a circle/ellipse/parabola/hyperbola depending ...
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1answer
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Does a spaceship traveling to Mars from Earth via orbital skyhook still have to wait for a transfer window? [closed]

In order for it to make the three months travel time does it still have to wait for a transfer window or can it go at any time of the year?
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Alfonso Gonzalezs Orbital mechanics simulation

I basically copied all the code on Orbital Mechanics Series of Alfonso Gonzalez (because I really don't have any experience with coding, but would like to in the future) on Youtube (for a school ...
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Is there a formula for converting a rocket's performance for one orbit to another? E.g. SSO performance to GSO?

If a rocket can take 1,000 kg to SSO at 500 km, is that enough information to determine what its capacity to, say, GTO or GSO would be? If so, how would one calculate it?
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energy needed to accelerate in space

I was thinking about possibility of cargo transport between, say, earth and mars when a “pusher” accelerates propulsion-less cargo vessel, which is catched and decelerated at the other end of ...
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1answer
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How to model payload deployment in General Mission Analysis Tool

I just started reading the manuals and doing the tutorials for GMAT. I'd like to use it to model deploying multiple satellites from a launch vehicle and see their resulting orbits. Searching the ...
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Is there an intuitive reason for why the shape of the orbit at perigee is the mirror image of that at the apogee?

Is there an intuitive reason for why the shape of the orbit at perigee is the mirror image of that at the apogee? It seems strange to me, because the situation is so different at the perigee compared ...
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1answer
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What is the acceleration in an orbit decaying due to air resistance relative to one not decaying?

This answer to Is there an upper limit for the internal size of space stations? has this paragraph: Finally, if you are stuck ["stranded" in the middle of a room in a space station filled ...
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Difference between rotated frame and rotating frame

Suppose we have a spacecraft orbiting around Earth and we neglect all effects of Earth's $z$-axis motion, i.e., no wobble, precession, or nutation. For simplicity, we only assume a rotation rate $\...
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How many burns does it take to reboost the ISS?

When the International Space Station is given a reboost, how many burns are performed? Is it a Hohmann transfer orbit, with one perigee burn and one apogee burn? Or is it one burn at apogee just to ...
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Launch Elements

I already know about the six Keplerian Elements that are fundamental to a planet's orbit around the Sun, and for a few weeks now, I thought I'd got it down. Then, I wanted to have some fun, and test ...
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Translate/shift ECEF coordinates given certain distance

I have some orbits in ECEF coordinates overlapped at the origin, and I would like to "move" some of them given a certain distance from the original orbit similar to the following picture: ...
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Difference between distance from Mars (Rmag) and B-plane R coordinate

I am running some GMAT simulations on Mars 2020 trajectory to Mars, following the ephemerides published by JPL. I create a target sequence and target the planet using the b-plane coordinates B and T. ...
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How fast could a stone be thrown using a sling while standing on the moon?

Similar to this question except not about using a machine: What payloads and launch speeds could a sling launcher get using modern materials on the Moon? How fast could a stone be thrown using a sling ...
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1answer
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Obtaining orbital parameters of a closed orbit given the characteristics of the arrival hyperbolic orbit

According to this paper (page 8) by ESA, given the $v_{inf}$, the right-ascension and the declination of the arrival hyperbolic asymptote, it is possbile to find a loci of pericenters of different ...
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Orbit Guardians - bs, right?

California-based Orbit Guardians is one of a small number of startups trying to tackle orbital debris. It's difficult to tell exactly what their plan is, but based on this animation, they seem to ...
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1answer
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Calculating the delta V budget from Earth to Mercury

Context While verifying a basic computation to compute the required delta V budget to get to Mercury I am experiencing some difficulties in interpreting the number 8650 m/s from Earth intercept to ...
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1answer
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Is there a (low-thrust) thrusting strategy to change a single orbital element alone?

In literature, I have found the optimal thrusting directions (in terms of pitch and yaw) for maximizing changes in each orbital element. These optimal changes, while maximizing one element, have an ...
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How will Juice substantially increase its inclination around Jupiter in January 2031?

The ESA video Juice’s Jovian odyssey linked below is quite interesting to watch. Around January of 2031 it substantially increases its inclination around Jupiter. Big inclination changes can be ...
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Covariance Matrix for Space Surveillance Sensors

I have been trying to study the uncertainties associated with the orbital elements for LEO satellites determined by various Space Surveillance sensors around the globe. However, I am unable to find ...
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1answer
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How can I edit the STK report output?

I have been dealing for a while on a report which is generated by STK. It contains basically time, azimuth, elevation and range data. Besides those data I need to also generate the theta and phi ...
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Where can one find the accelerations due to high-order terms of the geopotential model?

The expression for the orbital perturbation due to J2 ($\mathbf{a_{J2}} = [a_r \ a_s \ a_w]^T$) as well as its derived effect on the argument of perigee and the right ascension of the ascending node ...
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1answer
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How can I calculate the weight a aero-spacecraft occupant experiences during sub-orbital but non-ballistic trajectories?

Once in orbit, astronauts experience "weightlessness" relative to their capsule or space station because they are moving at the same orbital velocity as the surrounding spacecraft. I have ...

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