Introduction

NOTE: This is a very graphics-heavy post and may take some time to load.

Lagrange points are those points in the three-body system where the tug of gravity from the two primary bodies cancel out and any spacecraft stays in the same relative position with the two primary bodies. If you are in the rotating reference frame, there are periodic orbits that are not centered on either body or the barycenter, but instead about the Lagrange points. In this post, I’ll be introducing a subset of these periodic orbits for the Earth-Moon system. If you want a more complete introduction astrodynamics I highly recommend the following. I created this post using initial conditions from Greebow’s 2006 Masters thesis, and I highly recommend giving it a read. Here are the orbits in the Earth-Moon system being constructed one by one.

Note: Technically each family has an infinite number of orbits, I’m just illustrating a subset of the family in each orbit.

L1 – Periodic Orbits

The L1 Lagrange point is located between the Earth and the Moon. The Earth is in blue, while the Moon is in red. Both are scaled up in size as they would be hardly visible if properly scaled.

L1 Lyapunov Family

The L1 Lyapanov family is a planar series of orbits that are quite unstable.

L1 Northern Halo

The L1 Northen Halo family has a complimentary L1 southern family which is mirrored about the X-Y plane. These orbits become more stable as they become more perpendicular to the X-Y plane. The most perpendicular orbits are called the Near Rectilinear Halo Orbits (NRHO) and are being considered for NASA’s gateway space station because of their relative stability.

L1 Northern Axial

The L1 Northern axial orbits are also sometimes called the North-Eastern orbits because they have a right-handed curl to them. There is also an L1 Southern Axial family

L1 Vertical

The L1 Verticle family is very symmetrically pleasing

L2 – Periodic Orbits

The L2 Lagrange point lies just outside the moon. The orbits about the L2 Lagrange point are similar to those about the L1 Lagrange point but are slightly larger in size. Additionally, the L2 Lagrange point has an extra family of periodic orbits called the Butterfly orbits

L2 Lyapunov Family

L2 Northern Halo

L2 Northern Axial

Note that the L2 Northern axial family curls in the opposite direction as the L1 Northern axial family, causing it to sometimes be called the North-Western Axial family.

L2 Vertical

L2 Butterfly

The Butterfly family is unique to the L2 Lagrange point.

L3 – Periodic Orbits

The L3 Lagrange point is located on the opposite side of the earth from the moon. The L3 family of orbits is like the L1 family of orbits only much larger.

L3 Lyapunov Family

L3 Northern Halo

L3 Northern Axial

L3 Vertical

L4 – Periodic Orbits

The L4 and L5, equilateral Lagrange points are both stable in the Earth-Moon system. I’m only going to display the L4 periodic orbits because the L5 periodic orbits are just the L4’s reflected about the X-Z plane.

L4 Planar Family

L4 Northern Axial

L4 Vertical

Interactives

If you want to explore interactive verisons of these orbits you can click here for the orbits around colinear Lagrange points (L1-L2-L3) and here for the orbits around the equilateral Lagrange points (L4-L5)

Want More Gereshes?

If you want to receive new Gereshes blog posts directly to your email when they come out, you can sign up for that here!

Don’t want another email? That’s ok, Gereshes also has a twitter account and subreddit!

Share this: Facebook

Reddit

Twitter

Pocket

More

Print

LinkedIn



Tumblr

Pinterest



Telegram

WhatsApp



Skype

