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Lambert’s problem is concerned with the determination of an orbit from two position vectors - an initial point, \mathbf{R}_1; and a final point, \mathbf{R}_2 with radius r_1 and r_2, respectively; a known time-of-flight, \Delta T; and a central Keplerian gravitational field of known...

This is a short (but somewhat technical note) on the rather arcane subject of converting a point in the perifocal reference frame to a more general x-y-z reference frame using quaternions. To get the ball rolling, let's introduce the perifocal reference frame. The perifocal reference frame...

Here's a challenge that might appeal: NASA has proposed parking its planned LOP-G (Lunar Orbital Platform Gateway) station in a Near Rectilinear Halo Orbit (NRHO) and, from this station, allow lunar landers to target landing at any site on the Moon's surface. This raises interesting questions...

As many of the regular readers of this Maths & Physics forum will know, over the last six months I've been working on an exercise of 'mapping' the centre-manifold orbits (planar and vertical Lyapunov, Lissajous and halo orbits) of the L1 and L2 Lagrange points - particularly those of the...

This is a direct continuation of Station-keeping at Earth-Moon L2 scenario example Attached is a .zip file containing six station-keeping at Lagrange point scenarios. These scenarios are: 1. Earth-Moon L1 2. Earth-Moon L2 (already posted in the earlier thread but included again here for...

Following directly on from An update on all things Lissajous and Halo, attached is a zip file containing a scenario and associated script and data files for a demonstration scenario of station-keeping at Earth-Moon L2 Lagrange point. Download the zip file and, in the usual file, copy the files...

Over the last six months or so, I've posted a number of threads relating to general Lissajous and Halo orbits with a view to developing simple tools that can lock vessel onto a prescribed 'closed loop' orbit around the L1/L2 Lagrange points of the Earth-Moon, Sun-Earth and other restricted...

This is a second post detailing how to construct the state vectors of a prescribed Halo orbit around a Lagrange point. It is a direct continuation of the post Construct a Hal orbit around L2 of the Earth-Moon system so it's probably a good idea to read that post before reading this one. That...

OK, it's been some months since my last substantial post on Lissajous and Halo orbits; and, to be frank, it's also been some months since I last thought seriously about this topic. However, when I last wrote a post on Halo Orbits (way back on 30 October, 2018), I ended up by saying that (now...

In this note, I want to talk about the definition of Halo orbits in the context of the previous posts on Lissajous orbits: Dialing-up arbitrary Lagrange Point orbits Dialing-up a planar Lyapunov orbit Dialing-up a vertical Lyapunov orbit A digression on Lissajous orbits Sun-Earth General...

Attached is a .zip file containing .xlsx spreadsheets containing the datasets needed to calculate the state vectors of Lissajous orbits about L1 and L2 of the Sun-Vesta system in the Elliptic Restricted Three Body Problem (ER3BP). With these datasets, one can calculate the state vectors of a...

Attached is a .zip file containing .xlsx spreadsheets containing the datasets needed to calculate the state vectors of Lissajous orbits about L1 and L2 of the Sun-Mars system in the Elliptic Restricted Three Body Problem (ER3BP). With these datasets, one can calculate the state vectors of a...

Attached is a .zip file containing .xlsx spreadsheets containing the datasets needed to calculate the state vectors of Lissajous orbits about L1 and L2 of the Sun-Earth (EMB) system. With these datasets, one can calculate the state vectors of a vessel on the centre manifold of any given MJD for...

You may have noticed a steady trickle of posts on Lagrange Point orbits has appeared on Lagrange Point orbits. This is, of course, down to me attempting to explain how to use a high-order Lindstedt-Poincaré perturbative solution to the equations of motion in the restricted three-body problem...

This is a second follow-on post from Dialing-up arbitrary Lagrange Point orbits. In it, I'm going to demonstrate how to place a vessel in a vertical Lyapunov orbit around EM L2 using the tools described in the earlier post. The first follow-on post Dialing-up a planar Lyapunov orbit demonstrated...

This is a follow-on post from Dialing-up arbitrary Lagrange Point orbits. In it, I'm going to demonstrate how to place a vessel in a planar Lyapunov orbit around EM L2 using the tools described in that earlier post. (If you want to see an illustration of a planar Lyapunov orbit, see here: More...

This post presents a tool for 'dialing-up' Orbiter-friendly coordinates of arbitrary centre-manifold orbits (Halo, Lissajous, planar and vertical Lyapunov) around L1 and L2 of the Earth-Moon system in the Elliptic Restricted Three-Body Problem (ER3BP). Simply provide the MJD and the coordinates...

Over the last couple of months I've been busy working out the parametric representing the closed 'centre manifold' orbits of the L1 and L2 Lagrange points of the Earth-Moon and Sun-Earth systems. And I've just about finished. Essentially, this is a mapping exercise. Just as Keplerian orbits...

This note is going to be about building a high-fidelity integration engine for Orbiter that takes into account the gravitational influence of other bodies (tidal forces) and the 'non-spherical gravity sources' that Orbiter attributes to each body. In a subsequent post, I will show how this...

This note sets out the transformations that Orbiter uses to convert points in its 'body-centred inertial' (BCI)reference frame to its 'body-centred, body-fixed' reference frame. (The BCI reference frame is a generalisation of the Earth-centred inertial (ECI) reference frame applying to any...