Search results

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...

Hi, 'ncc1701d' The method used in the paper basically uses a complicated n-body numerical integration scheme to construct the perturbed Lambert solver. OK, so what dos this mean? Well, the paper's authors use a complex gravity model where they throw in as much detail as they can about the...

Further to 'martins' comments, the fact that you are approaching and flyby of Venus means that your gravity field is not Keplerian. This makes life more complicated. By far, the easier way to tackle this is to use what is known as a 'patched conics approximation' where you break up your points...

As per Thorsten, spline interpolation will work just fine as an approximate solution. Having said that, a somewhat less approximate approach is to use a Lambert Solver to determine the exact shape of the Keplerian (1/r^2) trajectory between each consecutive pair of your 13 points. Then one can...

Hi, 'ncc1701d' The short answer is yes, you would use a form of numerical integration. To describe a particular method, it would be helpful to have answers to the following: Is your gravity field a straight-forward Keplerian (1/r^2) gravity field or does it have solar and other perturbations...

No problem, malakai. Re extension to mixing elliptical and hyperbolic orbit: as I worked through the maths, I though that this extension was likely but I didn't have time to confirm it. So, thanks for considering these cases and confirming that it also works in the hyperbolic regime and (by...

I'm going to work through a number of examples and attach them to the relevant posts - so, even though the arcane maths may not be entirely clear, the mechanics of constructing the state vectors of a Halo orbit should be. After that, I'm going to show how to 'lock' a vessel onto a Halo orbit...

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...

Slowly getting over the jet lag and have had a chance to look more closely at your ('dgatsoulis') solution. When looking at these low-energy solutions, it often makes sense to transform the problem to rotating coordinates in which the position of the Earth and the Moon (in the case of the...

I read this while holidaying in Croatia recently. While driving on the freeway from Dubrovnik back to Zagreb to catch my return flight home, I pondered dgatsoulis' solution to the problem. Judging by the IMFD trajectory plan, what I think is going on is actually quite complex with the...

I assume that what you want to do here is to transform a velocity vector in the ECI reference frame to the ECEF reference frame. The general transformation of a position vector, Q_{ECI}(t), in the ECI reference frame to a position vector in the ECEF reference frame, Q_{ECEF}(t), is given by a...

Quite possibly. Having said that, it may not be the only way of achieving a ballistic transfer between L1 and L2. The argument runs something like this: 1. In the CR3BP model, for each planar Lyapunov orbit there is a conserved quantity which we will call C_1 for the L1 Planar Lyapunov orbit...

Thank, Ajaja. Nice work. Yes, there ought to be ballistic transfers from L1 planar Lyapunov orbits to L2 planar Lyapunov. As you've worked out, one ought to leave an L1 orbit on an unstable manifold trajectory and this should connect with a stable manifold tractor leading to an L2 orbit...