Space is Hard

From ionizing radiation to micrometeoroids, space is a dangerous place. Most spacecraft, when they feel threatened, can autonomously enter into a protective operating mode call safe mode. Different spacecraft do different things in safe mode, but most turn off all non-essential components, like propulsion and the payload, to focus all energy on trying to communicate with earth, and if it has solar panels, keeping them pointed towards the sun. One system that is often considered non-essential is propulsion, and if a safe mode event happens during a thrusting arc, it starts a missed thrust event (MTE).

A new generation of spacecraft want to take advantage of highly efficient electric propulsion systems which are more susceptible to these MTEs. Unlike traditional propulsion methods, which can produce a large amount of thrust in a short period of time, these high-efficiency engines can only offer fractions of traditional engines thrust. This means that instead of a burn taking minutes to hours, these engines will need to thrust continuously for weeks to months at a time. For a planetary rendezvous, these engines may even need to thrust continuously for the entirety of a trajectory. Low-thrust interplanetary trajectories are often years long, and a spacecraft has a 60% likelihood of entering a safe mode after 200 days

How do we Know About Safe Mode Events?

In 2018, a group of researchers at NASA’s Jet Propulsion Laboratory, Imken Et Al. (2018)(Note: it’s behind a paywall), looked at 240 beyond Earth safe mode events from a variety of missions and found that the time between safe mode events and the duration of those events corresponded to two Weibull distributions. Weibull distributions can be described by two parameters, shape and scale. I’ve reproduced the table from the paper below.

Long Duration Trajectories

Now that we have distributions for the time between events, and the duration of the events, let’s figure out how many MTE’s we can expect during a sample 1 year trajectory from Earth to Venus. To simplify we’re going to assume that the entire trajectory is a thrusting arc, which makes all safe mode events MTEs. We’re also going to calculate the expected number of MTE’s through a Monte-Carlo method. This means we are going to simulate a large number of trajectories, count how many trajectories had a specific number of MTEs in them, and then divide that by the total number of trajectories to get the probability that the specific number of MTEs will occur.

We can see that not only is 1 MTE the exected number of MTEs, but this trajectory is also more likely to have two MTE rather than no MTEs. Using this same method, we can also calculate how long the total duration of MTEs will be.

Evolving Over Time

By varying the length of the trajectory from half a year to five years, we can see how the expected number of MTEs change and how the distribution evolves.

Here we see how the expected value initially grows quickly but then slows down as it passes 3 years. An interesting question is “when do one and two MTEs become the expected values on a thrust arc?” Rubinsztejn Et Al. (2019) (Me!) place it at about 0.68 years and 1.3 years respectively.

As we’ve explored in this post, spacecraft that adopt new high-efficiency low-thrust propulsion techniques will need to be able to deal with multiple MTEs on long-duration thurst arcs. I’ve also created an interactive tool here so you can explore the expected number of MTE’s for different length thrust arcs

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