An Introduction to Beresheet and Its Trajectory to the Moon

This Thursday, April 11th, a washing machine sized-spacecraft will attempt to land on the Moon. If it succeeds, it will be the first privately funded spacecraft on the Moon, and make Israel the fourth country to land on the Moon after Russia/USSR, the USA, and China. This post will go over the basics of what SpaceIL / Beresheet is, why it’s going to the moon, and then spend some time exploring its trajectory. 

What is Beresheet?

In 2007, Google sponsored a $20 million dollar challenge for the first private group to land a spacecraft on the moon. In 2011 SpaceIL, a team from Israel, signed up for the competition. Since then they have been working on their spacecraft called Beresheet. In 2018 Google canceled their challenge as no one had completed it. SpaceIL decided that they were so far along with their development they would continue to work on Beresheet. In February of 2018, they launched as a secondary payload aboard a Falcon 9 rocket. Last week on April 4th, after a lunar orbit insertion maneuver, Israel became the seventh nation to orbit the moon

Note: they also do a lot of outreach like releasing a whole children’s book about their spacecraft.

Beresheet’s Trajectory

I went to spaceIL’s website and they have some great visuals for people slightly interested in their mission, but on this blog, I’ve dedicated a whole series to astrodynamics so I scraped their website to get Beresheets trajectory for a bit of a deeper dive. Here’s the trajectory in (what I’m pretty sure is) the Earth-Centered Inertial Frame

Now, this is an Earth-Moon system, so we’re dealing with 3-body dynamics. Let’s tease out some structure by converting it to an Earth-Moon rotating frame and then nondimensionalize it using the earth-moon distance.

There are a few things to note before we go onto looking at the different segments of the trajectory

•  I also translated the system so that the origin is now at the barycenter assuming μ = 0.0123 instead of at the center of the Earth
• There’s an out of plane component to this trajectory, but I’m only plotting the x-y plane because good non-interactive 3-d plots are much harder than good non-interactive 2-d plots.
• The original data has a realistic moon model which means it’s on an elliptical trajectory about the earth. All of the past work on this site has dealt with the moon being on a circular trajectory. I didn’t think it would be a good idea to go over the elliptical restricted 3 body problem in this post, so I’m forcing the moon to a constant distance from the earth. This introduces some weird forces/artifacts but is good enough for a blog post
• I was unable to find documentation from SpaceIL so some of the following trajectory analysis is just speculation on my part. 

Launch and Separation

Beresheet was launched as a secondary payload aboard a Falcon 9 and the trajectory below shows the spacecraft’s trajectory as it was attached to the Falcon 9’s upper stage.

Checkout orbits / Phasing

After being launched, the team at SpaceIL has two main tasks at hand. The first is checkout, which is where the team ensures that Beresheet is still functioning after launch. While they test spacecraft thoroughly before launch, there is always something that can go wrong during the extreme vibration loading during launch. 

Note: if you are interested in the nuts and bolts of spacecraft design and testing I highly recommend this book. It’s been in every satellite lab I’ve ever been in and I wouldn’t be surprised if SpaceIL had a copy or two.

After they determined it’s functioning, they need to wait for Beresheet to be in the right location for their next maneuver, which is why they go a few orbits that just precess around the Earth. You’ll notice that on this leg of the Beresheet trajectory, there’s an anomalous orbit. This lines up with where Beresheet was supposed to perform its first maneuver, but there was a software glitch. Instead, Beresheet had to wait for two more orbits to be completed for it to be in the proper location for its first burn.

Note: The earth is to scale in all of the images. The reason why some of the trajectories look like they intersect earth is once again because I’m only plotting the X-Y plane and not the full 3-D trajectory. If I was we would see that the spacecraft goes below the earth, and does not intersect it. 

Orbit Raises

To raise your apogee, it’s most efficient to burn when you’re at your perigee. While this could be done in one bur, Berehseet had to break it up into two for it’s less powerful thrusters. 

The first burn raises the trajectory a little but then the second burn really raises the trajectory and after a few orbits the spacecraft flies by the moon.

Lunar Orbit Insertion

This was the maneuver that occurred on April 4th. At this point, Beresheet had enough energy as it was flying towards the moon that it would have been thrown out of the Moon-Earth system if it hadn’t done anything. On this maneuver it thrusted against its path, trying to remove enough velocity to enter into orbit around the moon. This maneuver is called lunar orbit insertion (LOI)

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