Michael Paluszek is President of Princeton Satellite Systems. He graduated from MIT with a degree in electrical engineering in 1976 and followed that with an Engineer's degree in Aeronautics and Astronautics from MIT in 1979. He worked at MIT for a year as a research engineer then worked at Draper Laboratory for 6 years on GN&C for human space missions. He worked at GE Astro Space from 1986 to 1992 on a variety of satellite projects including GPS IIR, Inmarsat 3 and Mars Observer. In 1992 he founded Princeton Satellite Systems.

Electron density profiles on PFRC with USPR: Ultrashort Pulse Reflectometry (USPR) is a plasma diagnostic technique that would be used on the Princeton Field-Reversed Configuration (PFRC) to measure electron density profiles. Such profile measurements provide insight into the structure of PFRC plasma and can improve our estimates of confinement time. Our University partner is University of California, Davis, PI Dr. Neville Luhmann.

Evaluating RF antenna designs for PFRC plasma heating and sustainment: We intend to analyze RF antenna performance parameters critical to the validity of robust PFRC-type fusion reactor designs. Team member University of Rochester will support TriForce simulations and contractor Plasma Theory and Computation, Inc. will support RMF code simulations. Our national lab partner is Princeton Plasma Physics Laboratory, PI Dr. Sam Cohen.

Stabilizing PFRC plasmas against macroscopic low‐frequency instabilities: This award will use the TriForce code to simulate several plasma stabilization techniques for the PFRC-2 experiment. Our lab partner is PPPL and the team again includes the University of Rochester.

These awards will help us advance PFRC technology. Contact us for more information!

Princeton Satellite Systems has been marketing SunStation electric vehicle charging stations for some time. We are also EV enthusiasts. One employee owns a Tesla Model 3. I now own a Ford Mach-E. It replaces a Nissan Leaf that was purchased in 2012.

Before we purchased the Mach-E we looked at the Hyundai Ioniq 5, the Volkswagen ID 4 and the Kia EV 6. They are all nice cars. It was a close decision between the Mach-E and the Ioniq 5. The good thing is that there are many EVs from which to choose. Even within models, there are many options so that you can pick the car that meets your needs. EV-specific requirements are range, charging network, and charging speed. Otherwise shopping for an EV isn’t much different than shopping for any other car. EVs are available in almost every form factor, including pickup trucks like the Ford F-150 Lightning.

The Mach-E is a 2021 model rear-wheel drive Premium Model with an extended range battery.

This gives a range of 335 miles, 10% more than the EPA value.

The Level 2 charger is in the background. This is more than sufficient to reach all of the places we visit without charging along the route. The FordPass app will find a route for your trip and tell you when and where to charge. For our planned trips, it is showing that no en-route charging is needed, as long as we start near full charge. Tesla has an extensive Supercharger network that makes intercity driving really easy. All other EVs rely on networks such as ChargePoint and EVGo. There are many apps, besides FordPass, that will plan your trip including required charging stops.

We have a Level 2 charger at home that we bought for the Leaf. We also own a Prius Prime Plugin. The Prime is a plugin hybrid with about 30 miles range using the battery. The charging pattern during the week, when the Mach-E is used for commuting and shopping, is much like a gas car. We typically only charge the Mach-E once a week using the Level 2 charger at home. It takes about 10 hours to fully charge the battery. The Prius charges in 4 hours using a Level 1 charger. That is done daily.

If you owned a Mach-E and didn’t have a charger at home, it would mean you would only have to charge at a DC fast charger once a week if your driving patterns were like mine. If only Level 2 chargers were available, you’d need to find a Level 2 charger where you could park for 10 hours. In my town that would be hard because there only 6 Level-2 chargers!

Most recently we drove from Princeton to the Berkshires, then to Boston and then back to Princeton. The trips were made without any charging on the way. We used Level 2 chargers at our destinations. The Williams Inn, in Williamstown, had ChargePoint chargers, as did the Cambridge Marriott in Kendall Square in Cambridge, MA.

Our cars are charged mostly by our solar power system. This is supplemented by PSE&G’s network which gets a large portion of its power from a nuclear fission plant. We are working on compact nuclear fusion power plants. Perhaps, in the not too distant future one of our PFRC reactors will be the source of power for EVs.

Hohmann transfers are a well-known maneuver used to change the semi-major axis of an orbit. The Spacecraft Control Toolbox allows you to compute the required velocity changes, and integrate them into a full simulation.

In this demonstration, we create a 6U CubeSat that has 3 orthogonal reaction wheels and a single hydrazine thruster. The thruster is aligned with the body x-axis and must be aligned with the velocity vector to do the maneuver. An ideal Hohmann maneuver is done with impulsive burns at two points in the orbit. In reality, with a thruster, we have to do a finite burn.

rI = [-7000;0;0];
vI = [0;-sqrt(mu/Mag(rI));0];
OrbMnvrHohmann(Mag(rI),rF);
[dV,tOF] = OrbMnvrHohmann(Mag(rI),rF);

The first time OrbMnvrHohmann is called, it generates the plot below of the planned Hohmann transfer. The function computes the delta-V and also the time of flight, which will be used to determine the start time of the second thruster burn.

We create a short script with numerical integration to implement the maneuver using a thruster. The burn durations are computed based on the thrust and the mass of the spacecraft. In this case, they are about three minutes long. The maneuver is quite small, so the mass change is not important. The attitude control system uses the PID3Axis function which is a general-purpose attitude control algorithm. The simulation is a for loop, shown below. The ECI vector for the burn is passed to the attitude control system, which updates every step of the simulation.

% Simulation loop
for k = 1:n
% Update the controller
dC.eci_vector = uBurn(:,kMnvr);
[tRWA, dC] = PID3Axis( x(7:10), dC );
% Start the first burn
inMnvr = false;
if( t(k) > tStart(1) && t(k) < tEnd(1) )
inMnvr = true;
end
% Switch orientation
if( t(k) > tEnd(1) )
kMnvr = 2;
end
% Start the second burn
if( t(k) > tStart(2) && t(k) < tEnd(2) )
inMnvr = true;
end
if( inMnvr )
dRHS.force = thrustE*QTForm(x(7:10),dC.body_vector)*nToKN; % kN
else
dRHS.force = [0;0;0];
end
el = RV2El(x(1:3),x(4:6));
xP(:,k) = [x;tRWA;Mag(dRHS.force)/nToKN;el(1);el(5)];
% Right hand side
dRHS.torqueRWA = -tRWA;
x = RK4(@RHSRWAOrbit,x,dT,0,dRHS);
end

The maneuver logic just waits a quarter orbit then performs the first burn, by applying the thrust along the body vector. It then waits for the time of flight and then starts the next burn. The start and stop times are pre-computed. RK4 is Fourth Order Runge-Kutta, a popular numerical algorithm included with the toolbox.

At the final orbit radius an attitude maneuver is needed to reorient for the final burn.

The spacecraft body rates, in the body frame, during the maneuver are shown below.

The reaction wheel rates are shown below. The simulation does not model any particular wheel. Friction is not included in the simulation, although the right-hand-side function can include friction.

The wheel torques and rocket thrust are shown below. The thruster is a 0.2 lbf hydrazine thruster that is based on the Aerojet-Rocketdyne MR-103. The PID controller does not demand much torque.

The semi-major axis and eccentricity are shown below. The middle portion is during the transfer orbit.

The eccentricity is zero at the start and finish. Note the slope in both eccentricity and semi-major axis due to the finite acceleration. At the end of the simulation, we print the achieved orbital elements:

Final SMA 7099.72 km
SMA error 0.28 km
Final e 1.3e-05

The result is very close to the ideal solution!

This post shows how you can easily integrate attitude and orbit control. Email us for more information! We’d be happy to share the script. We can also offer a 30 day demo to let you explore the software.

Michael Paluszek of Princeton Satellite Systems, will talk about nuclear propulsion for space at the Foundation for the Future Zoom meeting on Thursday, May 19 at noon EDT.

The talk will discuss space propulsion and how fusion and fission power will revolutionize space exploration.

The Foundation for the Fusion has many other excellent speakers on both Wednesday and Friday of this week. Please join in!

I attended the ARPA-E 2022 Fusion Annual Meeting at the Westin St. Francis hotel in San Francisco. Here is the poster for our Princeton Field Reversed Configuration ARPA-E OPEN 2018 grant.

Here is our ARPA-E GAMOW poster on power electronics. It includes work by Princeton Fusion Systems, Princeton University, Qorvo and the National Renewable Energy Laboratory.

The meeting had two days of interesting talks by distinguished speakers. Dr. Robert Mumgaard of Commonwealth Fusion Systems talked about their work on advanced high-temperature superconducting magnets and the theory behind high field Tokamaks. Dennis Stone of NASA discussed NASA COTS programs. Dr. Wayne Sullivan of General Atomic talked about their research programs. General Atomics has been operating a Tokamak possibly longer than anyone else. We heard talks on the Centrifugal Mirror at the University of Maryland and WHAM, the high field mirror, at the University of Wisconsin. Andrew Holland of the Fusion Industry Association said FIA had verified 31 companies that were developing fusion power technology.

We talked to several organizations in need of high voltage and high current power electronics. We plan to pivot our GAMOW work to meet the needs of these potentially near-term customers.

The meeting had breakout sessions in which we discussed funding for fusion research and how to help gain social acceptance for nuclear fusion power. Both are challenging.

A third planet, as large as 26% of the mass of Earth, has been discovered orbiting our nearest stellar neighbor, Proxima Centauri .Astronomer João Faria and his collaborators detected Proxima Centauri d using the Echelle Spectrograph for Rocky Exoplanets and Stable Spectroscopic Observations.

It would be exciting to send a spacecraft to enter the Alpha-Centauri system and orbit this planet. At Princeton Satellite System we’ve looked at interstellar flight using the Direct Fusion Drive nuclear fusion propulsion system.

Interstellar Fusion Propulsion

At the 2021 Breakthrough Energy Conference we presented findings for both flyby and orbital missions. Flyby missions are easier, but orbit entry would allow detailed study of the planet. A flyby gets your spacecraft close, but it is moving really fast!

The following charts give an outline of our talk. The first shows the optimal exhaust velocity based on sigma, the ratio of power to mass. Our designs have a sigma from 0.75 to 2 kW/kg. With 2 kW/kg, the optimal exhaust velocity is 4000 km/s. The mission would take about 800 years. Our current designs can’t get exhaust velocities higher than 200 km/s. We’d need another method to produce thrust.

The next plot shows a point mission that reaches Alpha Centauri in 500 years. This requires a sigma of about 20. The spacecraft accelerates and decelerates continuously. The mission could be improved by staging, much like on a rocket that launches from the Earth into orbit.

The next figure shows how the starship would enter the Alpha Centauri system.

The final plot shows the orbital maneuvers that lower the orbit and rendezvous with the planet.

Even 500 years is a long time! This is over ten times the lifetime of Voyager, but much less than some engineering marvels built on the Earth.

We hope to someday be able to build fusion powered spacecraft that will head into interstellar space!

Moonfall is a movie coming out in 2022. It creates a scenario where the Moon’s orbit is changed and set on a collision course with the Earth. It is fun to work out the orbital mechanics.

Let us assume that the Moon is in a circular orbit around the Earth. It is actually more influenced by the Sun than the Earth, but the circular orbit approximation is sufficient for our purposes. A mysterious force changes the orbit from circular to elliptical so that at closest approach it hits the Earth. The transfer orbit has an eccentricity of 0.9673 and a semi-major axis of 195000 km. The new orbital period is 9.9 days so it will hit the Earth in 5 days!

What kind of force is needed? The required velocity change is 0.83 km/s so a force of 6 x 10^{16} N applied over 10 seconds is required. To get an idea of how large that force really is, the Space Launch System (SLS) Block 2 vehicle produces about 10 million pounds of thrust [1], which is approximately 50 x 10^{6} N (50 MN). Hence it would take 1.2 billion SLS rockets firing for 10 seconds to perform such a re-direction of the Moon! An image of the SLS is shown below (image from [1]).

As the Moon approaches the Earth it is going to raise the tides. A simple formula (really only valid when the Moon is far from the Earth) is

where is the gravitational constant for the moon, is the gravitational constant for the Earth, r is the distance between the Earth and Moon and a is the radius of the Earth. The distance during the approach and the wave height are shown in the following plot.

By around 3 days the tides started getting really big! We’d expect the Moon’s gravitational force also to pull on the solid part of the Earth’s surface, causing all sorts of trouble.

Version 2021.1 of Princeton Satellite Systems toolboxes for MATLAB is now available! Over 50 new functions and scripts are included. Many other existing functions have been improved.

One new function is AtmNRLMSISE.m, an atmosphere function based on the NRL MSISE model. It is uses extensive flight data and includes sun effects. It computes the overall density and the number density of all atmospheric constituents. Our function has an easy to use interface that automatically incorporates the sun information and lets you input your spacecrafts ECI coordinates. You can also choose to use the original interface. Here is a comparison with the existing scale height model.

We provide a complete set of functions for planning lunar missions in the Missions module. The software includes landing control systems and trajectory optimizaton tools. You can use our Optical Navigation system for your cis-lunar missions and explore our cutting-edge neural network terminal descent software.

Here are two images from an optical navigation simulation for a solar sail.

The Spacecraft Control Toolbox provides you with a lot of ways to do things, so you can use your own creativity to perform analyses or design a mission.

We just started our latest project for ARPA-E under the ARPA-E GAMOW program in which we will be build power amplifiers for fusion reactors. The goal is to lower the cost and increase the reliability of fusion reactor power electronics. We currently have grants under the DOE INFUSE program and another ARPA-E project that is part of the ARPA-E OPEN 2018 program. We just finished a NASA STTR grant to study the effects of plasma pulses on low temperature superconducting coils.

For those who have been following our work, you know that there are many articles and videos about our work. For your convenience, we’ve collected many of the URLs for them in this blog post.

2020 NJ Edison Patent Award (You’ll need to look for our award on this page. The others are interesting too!)

Space optical navigation employs a camera for attitude determination and a second high dynamic range camera on a pan/track mount for terrain and celestial body tracking. Navigation and attitude determination are performed in a Bayesian framework using anUnscented Kalman Filter with an IMU as the navigation and attitude base. The Optical Navigation Module provides MATLAB code for implementing optical navigation. Additional measurements can be added including a sun sensor for sun distance measurements in interplanetary space, Global Positioning System (GPS) measurements near the Earth, and range and range rate from ground stations or other spacecraft in deep space. The system is suitable for both lunar and Mars landing missions and icy moon and asteroid orbital missions such as Artemis, Lunar Orbital Platform Gateway, Orion Multi-Purpose Crew Vehicle, Europa Clipper, Lucy, Psyche. It is also applicable to any situation where GPS is not available.

The Optical Navigation Module allows you to implement an optical navigation system for any of these applications. It includes dynamical models for cis-lunar and deep space missions along with measurement models for all of these sensors. Several scripts provide examples to get you going quickly.

This picture shows the camera aimed at the horizon and the stars that it can see during Earth reentry. The step counter gives the integration step. The star numbers are sequential from the file of stars but the stars come from the Hipparcos catalog.

This pictures shows the laboratory hardware for an optical navigation camera on a pan/tilt mount. Flexible cables eliminate the need for slip rings simplifying the design. The platform is driven by orthogonal stepping motors with harmonic drives.

Note the size. As with all of our toolboxes, full source code is provided.