# Monthly Archives: June 2014

## Doppler Radar at Home: Experiments with a CW Radar Part 1

The radar I have outputs the doppler shift of a signal that is transmitted, reflected, and received.  Doppler is familiar to all of us as we hear the tone of a train horn or ambulance change as it rushes past us.  Since there is relative motion of the transmitter (horn) and receiver (your ears), there is a shift in received frequency.  Let's say that the source emits sound at a constant number of cycles per second (frequency).  Now let's suppose that the distance between you and the source begins to close quickly as you move towards each other.  The apparent frequency will go up because the source is closer to you each emitted cycle and you are closer to the source!

The doppler effect of a moving source. Image: Wikipedia

This particular radar transmits a signal at a frequency of 10.25 GHz.  This outgoing signal is continually transmitted and reflected/scattered off of objects in the environment.  If the object isn't moving, the signal returns to the radar at 10.25 GHz.  If the object is moving, the signal experiences a doppler shift and the returned frequency is higher or lower than 10.25 GHz (depending on the direction of travel).  This particular radar can be easily hacked and we can record the doppler frequency out of a device called a mixer.  The way this unit is designed, we can't tell if the frequency went up or down, just how much it changed.  This means we don't know if the targets (cars) are coming or going, just how fast they are traveling.  Maybe in a future set of posts, we'll build a more complex radar system such as the MIT Cantenna Radar.  Be sure to comment if that's something you are interested in.

Since we'll be measuring speeds that are "slow" compared to the speed of light, we can ignore relativistic effects and calculate the speed of the object knowing the frequency change from the mixer, and the frequency of the radar.

I took the radar out to the street and recorded several minutes of traffic going by, including city busses.  Making a plot of the data with time increasing as you travel left to right and doppler frequency (speed) increasing bottom to top, we get what's known as a spectrogram.  Color represents the intensity of the signal at a given frequency at a certain point in time.

Speeds of several cars on my street. 1000 Hz is about 33 mph and 500 Hz is about 16 mph.

The red lines are strong reflectors (the cars).  Most of the vehicles slow down and turn on a side street in front of the radar.  About 30 seconds in there are three vehicles, two slow down and turn, the third again accelerates on past.  Next I'll be lining up a video of these cars passing the radar with the data and you'll be able to hear the doppler signal.  To do that I'm learning how to use a video processing package (OpenCV) with Python.

In the next few installments, we'll look at videos synced with these data, radar signatures of people running, how radar works when used from a moving car, and any other good targets that you suggest!

## Gravitational Tricks: Lagrange Points and Orbiting at Puzzling Speeds

The orbital path of ISEE3 from launch to near present.

Last time I talked about a team trying to capture and reuse the ISEE3 satellite (here).  The team has received lots of telemetry lately, determined the rotation speed of the satellite, and even had an amateur radio operator receive the satellite!  While all of this is going on, they must rapidly plan out what orbit they wish to enter.  The most discussed orbit is termed ESL1, the Earth-Sun system Lagrangian point #1.  Lagrange points an interesting phenomena that I thought worth a short discussion.

When we think of orbits, traditionally we consult Kepler's laws.  These "laws" are 3 simple rules that were written down between 1609 and 1619 by Johannes Kepler.  I won't discuss them at length, because there are already many great sources to learn about Kepler's Laws and their application.  The thing we want to draw from them is that an object orbiting closer to the Sun (say Venus), will have to travel faster to satisfy the laws of nature.  In doing so it will orbit the Sun more times than the Earth will in the same amount of time.  Venus will in fact orbit the sun 1.6 times during 1 orbit of the Earth!

Let's say we place a satellite far away from the Earth, between the Earth and sun.  the satellite will orbit slightly faster than the Earth.  Over a period of time it will be on the opposite side of the Sun and we won't be able to communicate.  Eventually it will come around and lap the Earth! This isn't desirable, but we can use Lagrange points to solve this problem.

The simple laws of orbital mechanics that we have considered thus far are only valid for a simple problem with two objects (Earth and Sun or Earth and Satellite).  We have we three bodies though, the Earth, the Sun, and the satellite! Three body problems are generally sticky to solve, but we have an advantage.  The mass of a satellite is small compared to the mass of the Earth and the mass of the Sun (unless it's the Death Star).   We can ignore the small mass of the satellite as solve what is known as the restricted three body problem.  There are a few interesting points in space, the Lagrange points, at which the gravitational pull from the Sun and Earth are superimposed on each other to give the satellite the same orbital speed as the Earth!

The L1 point is where ISEE3 may end up, so let's look at it.  The satellite will be above the Earth at an altitude of 1.5 million km (932,000 miles), towards the Sun.  At this point, the two body mechanics say that the satellite will orbit the Sun faster than the Earth.  Adding in the complications of the three body problem, we see that the gravitational tug of the Earth towards the Earth,  away from the Sun is canceling out just enough of the Sun's pull to make the satellite orbit at the same angular speed as the Earth.  How useful!

There are other Lagrangian points as well (L2-L5), but we won't discuss them here, other than to say that a similar explanation can be given for each.  L4 and L5 are particularly interesting because they are inherently stable and hence lots of objects get caught there.  There are objects in Earth-Sun L4/L5 and Earth-Moon L4/L5.

Lagrange Points of the Earth-Sun system (Image: Wikipedia)

Generally satellites are placed in a small orbit around the L1 point for several reasons, including that it isn't inherently very stable.  The ISEE3 team will have to execute a rather complex series of maneuvers to get to L1 again, using the pull of the moon and making a very close pass that comes within 10's of km of the surface of the moon.  Time is of the essence, as the longer the wait the more they must change the speed of the craft (referred to as Delta V in the engineering jargon).  The ship only has about 150m/s of Delta V left before it runs out of fuel.  It'll take up to 1/3 of that to reposition the satellite, depending on how long the team must wait.

That's the quick and dirty view of Lagrangian points.  I hope this was interesting and helps you understand space exploration, or your addiction to Kerbal Space Program a little more!

## Reviving a Piece of the 1970's: ISEE-3

There's been a decent buzz in the space and tech communities about the "ISEE-3 Reboot Project", so I thought it would be worth mentioning here and pointing out some of wonderful techniques they are using to revive a satellite from almost 40 years ago.

The ISEE-3 satellite is one of three satellites that made up the International Cometary Explorer (ICE) program.  There were some interesting orbital things done with this satellite after its launch in August of 1978.  It was also the first spacecraft to go through the tail of a comet!  As with all missions, this one came to an end and the satellite was not head from since 1998.  The equipment to talk to the satellite was removed and it was considered to be out of service.

ISEE-3 sits in a heliocentric orbit, meaning that orbits the sun, not the Earth.  We knew that ISEE-3 would make another stop by our planet in 2014 when it was parked in this orbit in 1986 (from what I can tell anyway).  A group of citizen scientists started the ISEE-3 Reboot project, crowd funded on the internet.  They got permission to take over the satellite and intend to use the Moon's gravity and a rocket burn to send it on another mission.  If the window of June is missed, the satellite will probably never be heard from again.

The team was able to contact ISEE-3 on May 29 using the Arecibo observatory radio telescope.   The craft was commanded to transmit engineering telemetry, basically a health screening of the systems.  The team is currently busy decoding the data (streaming in at 512 bits/sec) and planning how they will execute the rocket burn.

The team is running out of an old McDonalds at the NASA Ames Research Park, the makeshift mission control has been termed "McMoons" after hosting previous space based projects.