PSS has been performing aerospace consulting since our founding in 1992. Our aerospace capabilities include consulting, MATLAB toolboxes, flight software and high-fidelity simulation, and CubeSat hardware development.
In 2015, astronomers from Caltech determined that a giant ninth planet may be orbiting the Sun. It was called Planet X and then Planet 9. The discovery was based on perturbations in the orbits of TNOs, trans Neptunian Objects. The planet has about the mass of Neptune and is in a 10,000 to 20,000 year solar orbit. Jakub Scholtz of Durham University and James Unwin of University of Illinois at Chicago hypothesize that Planet 9 might be a black hole. The orbit of Planet 9 looks something like this.
We used a semi-major axis of 700 AU, an inclination of 30 degrees and an eccentricity of 0.6. The plot shows the full orbit of Planet 9, but the simulation only shows 150 years of the other planets.
It would be very interesting to visit Planet 9. One way is to use a solar sail. The sail would start on a trajectory aiming at perigee very close to the sun and then accelerate at high speed. Another approach is to use a spacecraft propelled by Direct Fusion Drive, a fusion propulsion system we’ve been working on for several years. A 26000 kg spacecraft with a 12 MW engine and 2000 kg of payload could rendezvous with Planet 9 (based on the above orbit) in just 11 years. This is the spacecraft trajectory
Spacecraft with thrusters or instruments with large magnetic dipole will experience torques in a planetary magnetic field. U.S. Patent 10,752,385, just granted to Princeton Satellite Systems, uses a current loop to cancel the magnetic field of the onboard dipole. The patent text is:
“A dipole cancellation system and method may include a plurality of magnetometers for measuring a device magnetic field associated with a plurality of device coils generating a device magnetic field having a primary magnetic dipole moment. A compensating coil carrying a compensating current running a first direction that generates a compensating magnetic field having a compensating magnetic dipole moment. The compensating coil may be positioned and the first current may be selected so that the compensating magnetic dipole moment completely cancels the primary magnetic dipole moment. A method may use the system to stabilize a spacecraft by calculating an estimated torque of the spacecraft, receiving a value for an external magnetic field, receiving a value for a device magnetic field, and calculating and applying a compensating current may be then applied to the compensating coil to cancel the primary magnetic dipole moment, wherein the spacecraft is stabilized.”
Today, I will discuss two functions in release 2020.1 of the Spacecraft Control Toolbox (SCT) which can be used to get your spacecraft into a lunar orbit. They are LunarTargeting.m and LunarMissionControl.m. They are demonstrated together in the script LunarMission.m.
LunarTargeting.m produces a transfer orbit that starts at a Low Earth Orbit (LEO) altitude and ends up passing by the Moon with a specified perilune (periapsis of the Moon) and lunar orbital inclination. Its novel approach to the patched-conic-sections model of multibody orbital transfers uses the solution to Lambert’s problem to target a point on the gravitational boundary between the Earth and the Moon. Then it numerically optimizes over points on that surface until the initial velocity of the transfer is minimized. LunarTargeting.m requires the MATLAB optimization toolbox.
LunarMissionControl.m implements a control system which enables a spacecraft to propulsively enter lunar orbit. Like the other control systems implemented in the SCT, it stores its active state and degrees of freedom in a data structure, and accepts a list of commands as arguments. The commands we’ll see used here are ‘initialize,’ ‘lunar orbit insertion prepare,’ ‘align for lunar insertion,’ and ‘start main engine.’
LunarMission.m ties them both together and simulates a spacecraft, down to the attitude-control level. The simulation includes power and thermal models. The spacecraft can be controlled by reaction wheels or thrusters. Forces from the Sun, Earth, and Moon are included. The spacecraft starts on the trajectory returned by LunarTargeting.m, then acts in accordance to commands to LunarMissionControl.m. It takes the spacecraft 4.5 days to get to perilune, at which point it inserts itself into lunar orbit. Let’s take a look!
Take a look at the above figure. This is the entire mission trajectory in the Earth-Centered Inertial (ECI) frame. We can see the initial transfer orbit as the red line. Then it approaches the blue line (the Moon’s orbit), and begins corkscrewing around it after orbital insertion. Let’s look at that insertion in close-up:
The above figure shows the final part of the trajectory in Moon-centered coordinates. The red line starts as the spacecraft passes the imaginary gravitational boundary between the Earth and the Moon. It falls closer to the Moon, and at its closest point, fires its engines to reduce its velocity. You can’t see it in this figure, but that process is actually resolved on a 2 second timescale. The spacecraft is commanded to point retrograde using a PID controller, waits until it has pointed correctly, then fires its engines for a prescribed duration. If you look closely, you will see that moon has a 3 dimension surface courtesy of the Clementine mission.
Let’s finish this post off with some technical details:
On the far left, you can see the reaction wheel rates. They stay at zero for 4.5 days, as the spacecraft coasts. Then, when the craft is commanded to point retrograde for its orbital insertion, you can see wheels 2 and 3 spin up. Wheel 1 stays near zero; its vertical scale is 10^-16. Then in the center, you can see fuel use. The only fuel use is the insertion burn, so fuel stays constant until 4.5 days in. Less than 2 kg of fuel is used for this example, as the spacecraft is a 6U cubesat. On the right, the components of the body quaternion are displayed. Again, they are constant until 4.5 days in, when the craft is commanded to point retrograde.
I hope you’ve enjoyed this demonstration of how to simulate a lunar mission with the SCT! For more information on our toolboxes check out our Spacecraft Control Toolbox for MATLAB. You can contact us directly by email if you have any questions.
It is sometimes necessary to change your orbit semi-major axis, ascending node and inclination with a low-thrust engine. It is easy to do, as long as you can point your engine along orbit normal and tangential to the orbit.
It is easiest to see how this is done by looking at the Gauss’ Variational equations, simplified for small eccentricity.
I is inclination, is semi-major axis, is the gravitational parameter, is argument of perigee, is true anomaly, is ascending node. and the orbit tangential acceleration and is the orbit normal acceleration.
The resulting simulation is shown below. Mode 0 is semi-major axis change, Mode 1 is ascending node change, Mode 2 is inclination change and Mode 3 is off. It is best to change inclination and ascending node at the highest semi-major axis. You should change ascending node at the lowest inclination. The burns are done where the rate of changes are higher. Some change in inclination and ascending. node will happen when the other is being corrected.
The script for this simulation with the controller is part of the Spacecraft Control Toolbox Release 2020.1 coming in May.
A popular way of launching a small satellite is to bring it up on an International Space Station resupply mission. The Spacecraft Control Toolbox has functions to help you animate the orbit of your spacecraft near the ISS. A function, ISSOrbit, generates the orbital elements for the ISS. ISSOrbit generates Keplerian Elements from the latest 2-line elements. We use the function CoplanarOrbit to create an orbit 50 m below the ISS. There are no disturbances and the gravity model is for a point mass Earth.
DrawSpacecraft.m is a function that will draw any number of spacecraft in the viewer. This is the ISS and our, very small, NanoSatellite. The MATLAB camera controls allow you to zoom in or rotate the view. The view is with respect to the first satellite entered in the argument list, which in this case is the nano satellite.
DrawSpacecraft also does animation and will create an avi file. You can see the animation on our YouTube Channel or by clicking the video below. We converted the avi file to an mp4 file using a movie converter.
The script is an m-file that you can download, just to view, here.
NASA would like a crew to land on the moon by 2024.
We didn’t have time to write a proposal, but here is our design. We propose a single stage vehicle, that can land from and return to a 15 km circular orbit. It uses 2 Blue Origins BE-3U engines that use cryogenic hydrogen and oxygen. An Orion capsule houses the astronauts. The Orion would take astronauts to and from Gateway and to and from the Earth. Lockheed Martin is building the Orion spacecraft. The European Space Agency is building the service module. A separate transport would bring fuel and payload to the lander. In the future, the lander could be refueled from lunar water.
The dimensions are in meters. The Orion is shown below. We purchased the model from https://hum3d.com.
The landing gear were scaled from the Apollo Lunar module.
It is interesting to compare its size with the Apollo Lunar Module. The Artemis is designed to fit into the 10 m SLS fairing. This a fully reusable lunar vehicle that can be refueled. It is designed for a long-term, sustainable, lunar base.
We use two toroidal hydrogen tanks and two spherical oxygen tanks. The cylinder on the outside is the solar array producing 34 kW of power. Of course, numerous details are omitted. We developed this model using our Spacecraft Control Toolbox. The design script will be available in the Spacecraft Control Toolbox Version 2019.1 due in mid-November.
Other elements of the lander were designed for different purposes. The GN&C system is based on our Army Precision Attitude Control System.
Our control system is based on a robotic lander we designed some time ago. We have full C++ code for the control and guidance system.
The architecture for Earth/Moon transportation system is shown below. Eventually, a Direct Fusion Drive freighter would be the main way of moving cargo between Earth orbit, lunar orbit and Gateway. The lander would remain in lunar orbit. Humans would go to the moon using fast orbital transfer, much like during Apollo.
Our next blog post will show how we get from Gateway to and from our 15 km starting orbit. A subsequent post will demonstrate our lunar landing guidance that uses a neural network for navigation based on images of the surface. Using it for landing would require higher resolution images than we have today, but short of building a lunar GPS system, it might be more cost-effective to have a satellite assembling images from low lunar orbit.
We will also update this blog post from time to time. Stay tuned!
On May 29, 2019, Ms. Thomas gave an invited talk to the Future In-Space Operations working group on Direct Fusion Drive (DFD) for deep space propulsion. The slides and talk audio are available from FISO’s online archive here. The group hosts weekly telecon seminars to discuss upcoming technologies and their potential impact on space operations.
Our talk introduces Direct Fusion Drive, explains how it is based on the Princeton Field Reversed Configuration (PFRC), and reviews some potential missions. There are summaries of the key physics points enabling the PFRC and the computational and modeling tools we apply. We conclude with the roadmap to spaceflight, including the supporting technologies that will be required for successful space engines, like lightweight space radiators.
We’ve added some new tools to the Aircraft Control Toolbox for our upcoming 2019 release. The first is a new GUI for creating aircraft models. You import a Wavefront OBJ files and then you point and click to define leading edges, wing areas, engine locations and so forth. This makes it easier to import the geometric data. The GUI is shown below. It illuminates the view that you need to use for a given geometric element in red. The inertia matrix is generated from the mass and the surface geometry.
A new simulation function was added to use the data from this GUI. It has a flat Earth aircraft model with a plugins architecture. You can add your own lift, drag and thrust models or use the simple built-in models. It is much simpler than AC.m which is designed to be a comprehensive high-fidelity simulation. We’ve added a new animation GUI to show you the results of your simulations.
We expect 2019.1 to be available in June. You can get a demo with previews of the new functions now.
The Living Universe is both a feature film for IMAX theaters and now a four-part documentary series. We blogged about our interviews in January and the series is now available on Curiosity Stream, a service dedicated to documentaries! Episode 2,”The Explorers” features a segment on DFD narrated by PSS engineer Stephanie Thomas, in addition to discussing plasma and antimatter propulsion. Here is an article about the series from Broadway World. You need to sign up for an account on Curiosity Stream to watch, which is free for 7 days and then $3 per month.
“The Encedalus Mission” by internationally best-selling hard science fiction author Brandon Q. Morris was originally written in German, and features the DFD as the propulsion technology on a mission to study newly detected life in the Saturn system; an array of six DFDs power the spaceship. Early reviews are favorable! The book is available in paperback or for Kindle.
Send us a comment and tell us what you think if you watch the show or read the book!