About Michael Paluszek

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.

Visiting Planet 9

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

Direct Fusion Drive is based on the Princeton Field Reversed Configuration reactor invented by Dr. Samuel Cohen of the Princeton Plasma Physics Laboratory (PPPL). We have a experiment running at PPPL, funded by an ARPA-E OPEN grant, to perform critical ion-heating tests. Earlier work was funded by the NASA NIAC program. Hopefully we will be in a position to send a mission to Planet 9 in the not too distant future!

This analysis was done using the Spacecraft Control Toolbox v2020.1. Contact us for more information!

PSS Receives U.S. Patent 10,752,385, “Magnetic Dipole Cancellation”

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.”

For more information go to the U.S. Patent Site.

Lunar Helium-3 Return to the Earth

Helium-3 is available in the regolith of the moon and is a possible fuel for advanced nuclear fusion reactors on Earth. It would be extracted from the lunar regolith, packaged and returned to Earth. One question is how to return the helium-3 to the Earth. One approach is to use aerodynamic braking to return the helium-3 to a low Earth orbit where it would be picked up by the Space Rapid Transit (SRT) reusable launch vehicle and delivered to an airport where it would be shipped to power plants. SRT It is a two stage to orbit vehicle with a hypersonic air-breathing engine in the first stage.

The overall architecture is shown below.

One of the major advantages of SRT is that it can land and takeoff at any major airport. The first stage can be used as a transport vehicle. Since it is fully reusable and operates like an aircraft it is potentially much less expensive than vertical launch.

The return from the Earth involves launching the helium-3 tanker into orbit and then doing a departure burn that puts the spacecraft in an elliptical Earth orbit with a low perigee. As the return vehicle passes through perigee, aerodynamic drag lowers apogee until apogee and perigee are the same. This is shown in the following plots.

The first plot show the altitude from the Earth, the velocity magnitude and the drag force magnitude. The second plot shows the orbit. The last plot shows how apogee is reduced with each pass through perigee. It takes 10 weeks to enter the final orbit if the orbit perigee is 100 km. Note that perigee doesn’t change. The simulation uses a free-molecular aerodynamic flow model. For simplicity, it does not include lunar gravity perturbations.

Ideally, the lunar return vehicle would be brought back to Earth and reused.

The maneuver uses only drag. A lifting vehicle would have an additional degree of freedom since the force vector could be controlled.

This analysis was done with the Spacecraft Control Toolbox. The function will be available in Version 2020.2 available in early fall. Contact us for more information!

Hurricane Isaias 2020 and SunStation Solar Power with Battery Backup

Power went down when Hurricane Isaias moved in. Fortunately our customer had a SunStation solar power system with Lithium battery backup. Unlike other solar systems, this system has a transfer switch to disconnect the solar system from the grid so that the solar power system can power the house when the grid is down. The batteries provide enough power to keep critical systems going when it is really cloudy or at night.

You can see the system in operation here. The first shows the system when the solar power is insufficient to power the house.

The following shows the system with enough solar power to charge the battery and power the house.

Even on a cloudy day, you usually get enough solar power to keep the house running. The 0.2 kW load includes lighting, refrigerator, WiFi and other loads. This system has 14.4 kWh of storage, so it could run the house, without solar, for 72 hours.

For more information check out our SunStation page.

Toolboxes Version 2020.1 Now Available

Over 80 new functions and scripts were added in Version 2020.1. Updates were made to dozens of existing functions to improve their performance and expand their applications. Built-in demos and default data structures were added to many more functions. 

In the Spacecraft Control Toolbox, we added new tools for orbit control. The figure below shows a low thrust orbit raising starting from the ISS orbit and proceeding to a higher inclination, higher semi-major axis orbit. The controller also can change the ascending node. 

A new function, was added for animating spacecraft. The image below shows two spacecraft in formation.

A new function that provides the Keplerian elements for asteroids was also added.

Optical navigation demonstrations for Earth/Moon missions were added. this shows the centroid and lunar disk. The system uses a high dynamic range sensor that can see stars and the moon at the same time.

For operations people, a demonstration of one pulse nutation damping was added. Both roll angle and angular rate are reduce nearly to zero with one thruster firing.

The Aircraft Control Toolbox has many new features specifically added to support electric airplane development. This includes a new propeller efficiency model. 

Please contact us for more information! If you have purchased our toolboxes or updated your maintenance in the last year, the update is free!

Renewable Home Power, Backup, Heat and Air Conditioning

Princeton Satellite Systems has been in a leader in renewable energy with its SunStation home solar power system with battery backup. We introduced this product back in 2013. SunStation has lithium-ion phosphate batteries, the most stable and reliable batteries for home use. The core of the system is the Outback Inverter that seamlessly switches from grid power to internal power.

The solar system in the installation produces 7.3 kW of power, much more than the house needed for electric power including charging a Nissan Leaf and Toyota Prius Prime. The heating and air conditioning system was nearing its end-of-life so we decided to replace it with a geothermal heat pump. A heat pump is essentially an air conditioner that can both reject heat to a source and absorb heat from a source. The problem with both is that when the outside temperature is high, for rejecting heat, and low, for absorbing heat, the system loses efficiency. Modern air-source heat pumps are very efficient but do need backup resistance heating in some climates.

A ground source heat pump, or geothermal heat pump, uses the ground as the medium for absorbing or rejecting heat. The option we chose, due to land constraints, is to have two wells several hundred feet deep as the source. Alternatives are trenching, or a pond if you have one in your yard. The ground is always at around 50 deg F. The system was sized so that it rarely, if ever, needs resistance heating.

The geothermal system, which is made by WaterFurnace, was installed by Princeton Air. No changes to the SunStation were needed. The core geothermal system is shown below. The valves to the ground loops are in the foreground and the geothermal system is on the left.

The lines that run to the outside ground loops are shown below.

The system has a preheater for the (still gas) hot water heater. The gas water heater was less than a year old, so it didn’t make sense to replace it. The preheater is an electric hot water heater that does not have the heating coils connected.

The SunStation is shown below. The Outback inverter is on the bottom left. The boxes on top provide arc protection, which is now included in the inverter. The batteries on on the right and the battery management electronics between the inverter and the battery cabinet.

The well digging was quite a project. This picture shows the drilling rig.

This second picture shows the yard after the drilling was complete. Drilling took three days total.

The following system shows the SunStation with geothermal in operation. The Prius Prime is charging which is most of the load. The system is still sending considerable power to the grid. On average the house powers itself and two other houses.

Geothermal, with solar and battery backup is the ideal solution for new homes and for renovations to existing homes. There is no reason to even have a gas hookup anymore. Contact us at SunStation for more information


Yes, that is the name of the very famous computer game.

In our last blog post we talked about optical navigation for lunar missions. Optical navigation is also very valuable for asteroid missions. It is being used today on OSIRIS-REx. The system we developed can be used anywhere in the solar system without, hopefully, too much attention from the ground.

Now that you’ve decided to go to an asteroid, where are they? As it turns out there is a fabulous website with a downloadable database of asteroids http://naic.edu/~nolan/astorb.html. You can download a file with thousands of asteroid.

In Version 2020.1 of the Spacecraft Control Toolbox, we’ve added a function to plot the asteroids. It reads the file and returns the orbital elements, name, number and epoch. Here are two examples of asteroids in motion.

Ceres is the most famous asteroid. You may find one named after you! If you want the bigger picture, here is a second plot with 1000 asteroids. The circles are the orbits of Earth and Jupiter. The function will propagate all the asteroids you select if you don’t request any outputs.

Contact us for more information!

Optical Navigation to the Moon

There is great interest in lunar missions. The U.S. plans to land astronauts on the moon in this decade. Several commercial companies are working on landers. Many other national space programs are working on their own landers and rovers.

As with all spacecraft, you need to know where you are. The traditional way is to use a communications link from the ground to get range and range rate (via Doppler shift.) This works well but you need to collect data over a long period of time to get an 3-dimensional fix.

Recently, NASA discovered via the Magnetospheric Multiscale Mission (MMS), that GPS could be used at altitudes higher than the GPS altitude, and maybe all the way to the moon!

Princeton Satellite Systems developed an Optical Navigation System for NASA as part of an SBIR project. It uses two cameras. One is a navigation camera mounted on a 2-axis gimbal that looks for nearby planets or asteroids. A second camera points out of the orbit plane just looking at the star field. The navigation camera has sufficient dynamic range so that it can image a planet or moon and still see stars. The whole system works as a sextant, that has been used by mariners for hundreds of years. The Apollo astronauts used a sextant for backup navigation. Our system automates the process so that it is fully autonomous. Our simulations for the SBIR were for deep space missions, like simulated NASA Messenger and New Horizons spacecraft, and for communication satellites.

Recently we’ve customized the system to lunar missions. The following images are from a MATLAB script that simulates a transfer from the Earth to the Moon. The first is from the star camera pointing out of the orbit plane. The numbers are the star id from a list and don’t correspond to numbers in the Hipparcos Catalog which is used for the star simulation.

The second is the navigation camera, that points at the moon. The star moves as the relative angle changes. The circle around the moon is its disk.

The third shows the trajectory. It starts from behind the Earth. A lunar orbit insertion is done when the spacecraft reaches the moon.

Here is the spacecraft in lunar orbit.

The simulation runs until the spacecraft reaches the moon. The following video shows the simulation in action.

The simulation uses functions coming out in the 2020.1 release of the Spacecraft Control Toolbox. Contact us for more information!

Rendezvous Made Simple

In the “good old days” the only people worried about rendezvous were those designed space missions with crews. ISS established the need for robotic rendezvous and docking on a regular basis.

Orbit dynamics can be complex. If you are looking at rendezvous with any other spacecraft in a very different orbit you can start with Lambert’s Time-of-Flight algorithm. Given initial velocity and position vectors, and desired final position and velocity vectors and time of flight, it will give you the initial impulse velocity change needed to rendezvous. There are numerous formulation as it is complex math problem.

If you happen to be close to your target you can formulate your orbits as a relative orbit problem with Hill’s equations, shown below in state space form.

n is the orbit rate of the target spacecraft. x, y and z are the position of the “chase” spacecraft in the Hill’s frame. a is the control acceleration. You want to reduce the positions and velocities to zero. This can be done with a Proportional Derivative (PD) Controller, or with a Linear Quadratic (LQ) Controller. If your chase and target spacecraft have GPS it is relatively easy to find this state vector in the above equation. A PD controller will ignore the coupling in the above equations while the LQ will accommodate the coupling.

It is interesting to look at the gain matrices for the two cases and the corresponding eigenvalues. We tweaked the PD to make its position gains close to that for the LQ. The PD is designed for a damping ratio of 1. The eigenvalues are identical. The cross-axis gains are small, but non-zero.

Gain Matrix LQ
0.0032 -0.0001 -0.0000 0.0796 0.0000 -0.0000
0.0001 0.0032 -0.0000 0.0000 0.0796 -0.0000
0.0000 -0.0000 0.0032 0.0000 -0.0000 0.0796

LQ eigenvalues
-0.0398 + 0.0409i
-0.0398 – 0.0409i
-0.0398 + 0.0386i
-0.0398 – 0.0386i
-0.0398 + 0.0397i
-0.0398 – 0.0397i

Gain Matrix PD
0.0036 0 0 0.1200 0 0
0 0.0036 0 0 0.1200 0
0 0 0.0036 0 0 0.1200

PD eigenvalues
-0.0398 + 0.0409i
-0.0398 – 0.0409i
-0.0398 + 0.0386i
-0.0398 – 0.0386i
-0.0398 + 0.0397i
-0.0398 – 0.0397i

The simulation results for the LQ are:

And for the PD are:

The results are very close. The PD has no overshoot, as expected. The LQ is slightly faster but has some overshoot. Both get the chase spacecraft to the target in a few minutes, assuming, of course, that you have the acceleration capability shown in the plots.

Both are linear controllers. You can approximate a linear controller with thrusters by using pulse width modulation. An issue will be the minimum impulse bit of the thrusters, that will lead to a minimum velocity and position error that can be achieved.

This script is included in the Spacecraft Control Toolbox 2020.1 coming soon!

Flying Near the ISS

Many small satellites are launched from the ISS or near the ISS by one of the transfer vehicles. A new function in the Spacecraft Control Toolbox 2020.1, coming in May, allows you to visualize your spacecraft near the ISS. Here is an example. You can also display a trajectory.