Questions tagged [celestial-mechanics]

Questions regarding the movements and interactions of astronomical bodies as it relates to spacecraft, their trajectories, and their maneuvers. For the motion of spacecraft themselves, see [orbital-mechanics].

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71 views

Can the location of an unknown planet that is absent from a planetary system be calculated from the orbits of the remaining planets?

In the book ‘Seeker’ by Richard McDevitt, two characters search for a lost planet. They know the star system currently has a number of celestial bodies in orbit around it and their orbits are ...
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How to calculate the maximum heliocentric speed during a flyby?

The following graphs are related to the Voyager 2 / Jupiter flyby occurred on July 1979 (I did the calculation with the SPICE library and NAIF’s data files). We see that the maximum speed relative to ...
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1answer
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Could the orbit of a satellite place it on the z-axis of the ECI coordinate frame (x=y=0)?

It is mostly a hypothetical question; I assume the answer is no, but I am looking for any data to contradict my claim that there are none or at most only one satellite at a time which could ever ...
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How is it possible to connect trajectories at a Poincare section using the “bisection” method?

When constructing a heteroclinic connection (a connection between two different periodic orbits at two different libration points), the stable and unstable manifolds of two different libration points ...
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What does the term “libration point gateway” mean?

In the Circular Restricted Three Body Problem, natural paths exist between periodic orbits or the libration points that have negligible cost. These are commonly known as free transfers between ...
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Is the Jacobi constant stationary along a periodic orbit?

In the book called "Chaotic Worlds: from Order to Disorder in Gravitational N-Body Dynamical Systems", link here, the author states that if the dynamical system has an integral of motion which is not ...
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What is the physical interpretation of the eigenvalues of the monodromy matrix and how are they associated with the invariant manifolds?

To define the monodromy matrix, assume that the period for one cycle of a halo orbit is denoted as $T$, the initial time as $t_0$, and the state-transition matrix is defined as $\phi$. Then, the ...
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373 views

Calculate flight path angle given semi-major axis, eccentricity and distance from the focal point

How can I, given the semi-major axis (α), the eccentricity (ε), and the distance from the focal point (r), calculate the flight path angle (φ)? (As shown above)
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How can you construct the periodic orbits around libration points L1 and L2 in the circular restricted three-body problem and prove their existence?

Following up on a previous question about the classification of periodic orbits, how can they be constructed, especially the planar Lyapunov family, around libration points $L_1$ and $L_2$? And how ...
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171 views

What is the analytical closed-form solution of the two-body problem to verify its numerical integration results?

The purpose is to study the motion of two celestial bodies analytically. What is the closed-form of the two-body problem if I was to solve it analytically without using a numerical approximation ...
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Why does the Sun track out a seemingly sinusoidal path on the celestial sphere? [closed]

I know it's somehow related to the way things are projected but it hasn't quite clicked yet. The question arose because I wanted to understand the path of the eclipitic after reading about it here: ...
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Why is FORTRAN recommended for astrodynamics rather than MATLAB?

I understand that FORTRAN might be faster in terms of computation time, but I don't understand why it is always recommended by people in the field. Everyone tends to avoid MATLAB for astrodynamics; is ...
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1answer
169 views

Geocentric latitude and longitude of sub-satellite point

I was trying to derive the expressions for the geocentric latitude and longitude of the sub-satellite point using Keplerian elements. The final equations connecting the combination of the Keplerian ...
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STK Astrogator Earth Flyby

TLDR: How do you set up an EEV maneuver, specifically, how do you go from an earth orbit to a heliocentric orbit with a periapsis within Venus’s orbit in astrogator? I know the theory but astrogator ...
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1answer
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What does “Poisson's formula” refer to in this calculation?

I am not entirely sure if this question belongs to this forum, but I don't know where else to ask. I am following a Rocket Propulsion course. There is a section concerned with the Velocity ...
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3answers
874 views

Do Kepler's laws of planetary motion apply also to satellites of the Earth?

Do Kepler's laws of planetary motion apply also to satellites in orbit around the Earth? I would assume yes, but I'm not sure why...?
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1answer
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C3 calculation in interplanetary missions

I'm starting to study Astrodynamics and I'm trying to make a Porkchop plot for a Mars mission to compare the results with actual porkchop plots which I found on the internet, so I know if my ...
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How to get the coordinates from NASA JPL Ephemerides DE430 ( ECRS) to ECI?

I'm trying to make a software that determines the orbit of a satellite which is affected by the Sun and Moon. The coordinates [x y z] that I have for the satellite are in Eci. For the position of the ...
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374 views

How to derive the differential equations of motion for a dumbbell system ,eg. dumbbell satellites around earth?

From Eq. 2.13 from Orbital Mechanics for Engineering Students (Curtis, 2005) the equation of relative motion between two bodies orbiting around a center of mass can be written as: $$\ddot{\mathbf{r}}...
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What are the perihelion and aphelion distances of the Falcon Heavy second stage?

What are the perihelion and aphelion of the Falcon Heavy second stage containing the Tesla after yesterday's mission?
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1answer
337 views

Planets positions determination

I am writing a 3D solar system simulator that features planets, asteroids, comets and Trans-Neptunian objects. It also includes daily "Close Approach" bodies from the Jet Propulsion Laboratory ...
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1answer
117 views

Calculate NEO object position with nasa Near Earth Object data

I am using the nasa NEO object data: Listing Of NEO's: Nasa NEO Data Specific NEO Data: Object Data Given the information in this JSON data. Is it possible to calculate the position of the NEO in ...
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How to calculate the time of closest approach between two orbiting objects

I have two objects each one moves in elliptic orbit I calculated the distance of closest approach using (the minimum intersection disatnce).Knowing the true anomalies for both objects corresponding to ...
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Besides retarded gravitation, anything else to worry about when calculating MU69's orbit from scratch?

For fun I'd like to use Hubble Astrometric data for example the observations listed at the bottom here to numerically estimate the orbit of 2014 MU69 as well as its uncertainties. My plan is to use ...
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1answer
625 views

Restricted Three body problem need to create an orbit around the two massive bodies

I have assignment and part of it involves getting a satellite to orbit both the Earth and the Moon at least once. How ever no matter how I set my initial condition or parameterize my position and time ...
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Ephemeris for lunar body-centered body-fixed coordinates?

I'm going to try to do a modest simulation of the Moon's libration as seen from the Earth (geocenter), similar to the technical one's I've shown in this question. I'll do it in Python and render it in ...
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Understanding formula for geocentric position of Moon

I am trying to understand a basic formula in a Celestial Mechanics reference. The formula is for the position of the Moon in a geocentric frame. The reference claims in line (981) that this should be ...
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3answers
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What would be the effect of increasing the mass of Mars?

It seems to me, that if we want to make Mars as Earthlike as possible, we should increase its mass. The long term affects of lower gravity environments on humans is not fully known, but we have enough ...
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Python API for JPL Horizons?

I found the python package HorizonJPL in the Python Package Index, but it looks like it's limited to activity in 2013. When I go to the linked documentation page https://docs.google.com/document/d/...
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1answer
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“Pythagorean Three Body Problem” - need some points from an accurate solution for comparison

note: if you up-vote (or even if you don't), don't forget to scroll down and see the excellent answer as well - it's beautiful! The Pythagorean Three Body Problem also know as Burrau's problem is a ...
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Is Mercury's orbit still considered potentially unstable (in the very long term)?

The subsection Mercury–Jupiter 1:1 perihelion-precession resonance in the Wikipedia article Stability of the Solar System links to the article Solar system could go haywire before the Sun dies in the ...
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Source for up-to-date values of Mars' standard gravitational parameter

Wikipedia currently gives the standard gravitational parameter of Mars as: $$ GM_{Mars} = 4.2828(9) *10^{13} (m^3/s^2)$$ The (9) is the uncertainty of the last digit, so it works out to about ...
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Understanding gravitational keyhole analysis for Near-Earth Objects

I've been studying the resonant return and gravitational keyhole analysis for NEOs and using the extension of Öpik's theory of close encounters (aka Öpik-Valsecchi theory, Valsecchi et al., Astron ...
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Would an asteroid collision affect Moon's orbit, and what consequence would that have for Earth?

If an asteroid collided with the Moon, or an atomic bomb was blasted on it, would it affect the orbit of the Moon? The Moon's gravity plays a major role in ocean tides. If the Moon's orbit changed, ...
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1answer
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Have there been any photos taken of a total Earth-Sun eclipse from the Moon, or its vicinity?

There's a supermoon lunar eclipse ongoing right now (Sept. 27/28, 2015), and it got me thinking that a great way to show to people why the Moon is reddish -- when eclipsed by the Earth -- would be if ...
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Which of the planets could we detect today from just the movements of the sun?

Assume that despite our current level of space exploration and technology, we have somehow missed the existence of the other planets in our solar system. We have developed various methods of ...
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1answer
3k views

Does the Sun actually move on its own, or does it move with the Solar system? [closed]

I'm curious, does the Sun actually move? The concept behind the question is, if you wear a shirt and you move, does the shirt actually move? Like the Solar system orbits around the Milky Way, but does ...
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1answer
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Galactic location from spectrum and red/blue shift

I recently realized that the state of the galaxy as we perceive it from Earth is entirely unique; because of relativity, celestial objects are all viewed with out of date information, but as we ...
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Why is Uranus's rotation 98° to its orbital plane? [closed]

In pictures of Uranus you can see that its rings are give or take 98° to its orbital plane unlike the rings of Saturn and Jupiter. Also on Uranus's upper atmosphere, you can see darker bands at the ...
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1answer
570 views

With what forces are Saturn's Rings cohesively held together? [closed]

With what sort of gravitation are Saturn's Rings held together? It is very spectacular and intriguing compared to the way Earth's gravitation acts. I do not have a basic or conceptual idea of what/...
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Planetary migration due to tidal forces

The fine U. Washington article Some potentially habitable planets began as gaseous, Neptune-like worlds mentions twice that tidal forces can induce inward planet migration. Two phenomena known to ...
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Why does the Earth lose rotational velocity in the vacuum of space?

I think it is a well-known fact here that the Earth is slowly losing rotational velocity over time (some 1.4 milliseconds of the day are gained per hundred years). Eventually, this means that the ...
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1answer
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What stabilises the axial tilt of planets?

All known bodies of the space rotate around their axis. For example, Earth completes a full rotation cycle in about 24 hours. However, the axial tilt seems to be constant, even though it changes a ...
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1answer
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Are there any man-made satellites at Lagrangian points?

There are 5 lagrangian points. Are there any man-made satellites at any of those points? Is there a reason for the presence or absence of satellites at these points?
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Why is momentum transferred to the moon?

The moon whizzes around the Earth, dragging water after it and producing tides. In a comment on this question, I asserted this would sap the momentum of the moon causing it to fall to Earth. This was ...
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What is the escape-velocity for our galaxy?

What should be the escape velocity for our galaxy and can we calculate it? For instance, if we assume that we don't know the mass of our galaxy, you may consider it as small 'm'.
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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 ...