|Mars Pathfinder Trajectory Figures|
|Landing Footprint Plots|
The figures below illustrate the target landing area for Mars Pathfinder and the uncertainty of the pre-landing navigation solutions mapped to the surface of Mars. The desired landing area and navigation uncertainty are represented as ellipses, or footprints, overlayed on a Viking image (M120N032) of the Ares Valles area on Mars. The spacecraft was targeted to land at the desired site of 19.43 deg N (areographic) latitude and 33.1 deg W (or 326.9 deg E) longitude, which is marked by the red diamond in the image. Although we did the best we could to get the spacecraft to that target, we had to allow for some uncertainty in the conditions of our entry and descent through the atmosphere. Our goal was to land within the blue ellipse centered at the target site. This ellipse is 200 x 100 km (124 x 62 mi) and its orientation is determined by the geometry of the spacecraft's orbit at atmospheric entry. (To get a better idea of the size of this ellipse, take a look at its projection onto southern California shown below.)
The red (or other colored) ellipses represent our uncertainty about the spacecraft's trajectory. We took our best estimates of the trajectory at various times prior to landing and the errors associated with them and propagated these data forward to the point of atmospheric entry. We then took the dispersions in the state at entry and mapped them down to the surface to get an idea of how close we were coming to our target site. We represented our confidence in the solution by multiples of something called "sigma". The greater the number of "sigmas" you use, the higher is the probability that the spacecraft would land inside the red (or other colored) ellipse. A "1-sigma" ellipse represents a 39% change of landing inside the ellipse area while a larger "3-sigma" ellipse represents a 99% chance.
The uncertainty ellipses grew smaller as we got closer to Mars and, ultimately, became much smaller than the target (blue) ellipse of 200 x 100 km. In fact, I am able to show only 3-sigma ellipses from solutions within the last week before landing. But that's just part of the story - the centers of the ellipses also moved around with time. We kept tracking the spacecraft and doing trajectory solutions and we saw the predicted landing point wander around a bit. This was expected. The motion slowed over time and the solutions during the last 24 hours before landing were very stable, mapping very close to the same landing locations.
The red ellipse on this image represents a navigation solution using all tracking data from February to July 4, 1997 at 15:30 UTC (just prior to atmospheric entry). It represents our best navigation solution to date. The ellipse has shrunk to its smallest size since we have incorporated data from all 3 DSN sites during the last 24 hours. The data from the DSS 65 pass (in Madrid, Spain) beginning about 4 hours before landing is especially powerful. The ellipse represents the 3-sigma uncertainty and is 15 x 8.4 km (9.3 x 5.2 mi) in size. The ellipse is centered at 19.22 degrees N and 33.4 degrees W (326.6 degrees E). This is about 22 km (14 mi) from our target latitude and longitude.
The cluster of orange points on this image represents the uncertainty in our navigation solution that incorporates variations in the conditions during the descent through the atmosphere. This includes changes in the properties of the atmosphere itself such as pressure and density variations and changes in the vehicle aerodynamic characteristics such as lift and drag coefficients. If you imagine an ellipse enclosing the orange collection of points, you can see that it is larger than the red ellipse generated by our mapping of the interplanetary trajectory to the surface. These effects were always there, but they were very small contributors to the overall uncertainty until rather late in the game. It wasn't until we had the last few hours of data before entry that our traditional "navigation" uncertainty became small enough for the descent perturbations to make a significant contribution to the landing uncertainty. (The orange points were computed by Bobby Braun from NASA Langley who participated in the EDL activities here at JPL as the fourth member of our navigation team.)
The green and yellow X's on this image represent two different post-landing solutions for the landing site. The yellow X is the lander location derived from triangulation of features (large rocks, crater rims) visible in the pictures taken by the lander camera. (Here is an image zooming in on this region at higher resolution and pointing out some of the landmarks used to locate the spacecraft's position.) The green X is a (very) preliminary estimate of the lander location based on tracking data obtained from the lander in the first 2 days after landing. (Yes, we are still getting Doppler and, occasionally, ranging from the lander on the surface of Mars.) The points marked by the X's are roughly 27 km (17 mi) from the target latitude and longitude.
As you can see, there is some disagreement between our final navigation solutions using data before landing and estimates of the landing site using data after landing. This is not at all unusual. There are many assumption and models that we use to relate locations in interplanetary space to locations on the surface of a planet. Small errors or changes in any of these could account for this discrepancy. This just means we're not quite out of a job yet :-) We are now working with the science teams to resolve this. When we figure it out, I'll let you know.
The 7 smaller, colored ellipses clustered in the lower left corner on this image represent navigation solutions done between July 2 and 4, 1997. The first 6 represent our best estimates used to make several critical decisions during the period leading up to entry, descent, and landing (EDL). The times and events associated with each ellipse are:
Ellipse Time (PDT) Event ----------------- ------------- ------------------------------------- Green (2,largest) July 2 3 PM EDL flight software parameter update #1 Cyan (3) July 3 3 PM EDL flight software parameter update #2 Red (1) July 3 9 PM TCM 5A Light blue (7) July 3 11 PM EDL flight software parameter update #3 Orange (6) July 4 2 AM TCM 5B Lavender (4) July 4 5 AM EDL flight software parameter update #4These are listed in order of decreasing size. FYI, only the first parameter update was sent to the spacecraft and TCM 5 was not needed. The 7th ellipse - yellow (5,smallest) - represents our best solution using all of the pre-landing tracking data. It was done around 1 PM on July 4, after our successful landing.
As you can see from the figure, our navigation solutions were very stable from July 3 through the early morning of July 4. The slight change seen in the final solution represents the added information from the last tracking pass which began about 4 hours before entry. The ellipses all represent the 3-sigma uncertainties. Here are the sizes and centers of each ellipse:
Ellipse Size Center ----------------- ------------- ------------------------------------- Green (2,largest) 154 x 52 km 19.00 deg N, 326.3 deg E (33.7 deg W) 94 x 32 mi Cyan (3) 113 x 37 km 18.95 deg N, 326.2 deg E (33.8 deg W) 70 x 23 mi Red (1) 98 x 19 km 18.97 deg N, 326.2 deg E (33.8 deg W) 61 x 12 mi Light blue (7) 98 x 17 km 18.97 deg N, 326.2 deg E (33.8 deg W) 61 x 11 mi Orange (6) 98 x 14 km 18.98 deg N, 326.2 deg E (33.8 deg W) 61 x 9 mi Lavender (4) 97 x 13 km 19.01 deg N, 326.2 deg E (33.8 deg W) 60 x 8 mi Yellow (5,smallest) 15 x 8.4 km 19.22 deg N, 326.6 deg E (33.4 deg W) 9 x 5.2 mi
This solution was done on 6/30/97 - 4 days before landing and 5 days after the execution of TCM 4. As you can see from the position of the red ellipse, we were still on target for the desired landing site. The ellipse represents the 3-sigma uncertainty and is 179 x 68 km (111 x 42 mi) in size. The ellipse is centered at 19.5 degrees N and 33.1 degrees W (326.9 degrees E) - once again, pretty close to our target of 19.43 deg N and 33.1 deg W (326.9 deg E).
The solution was done on 6/26/97 with a little less than 24 hours of tracking data taken since the execution of TCM 4. As you can see from the new position of the red ellipse, TCM 4 had moved the spacecraft back on target for the desired landing site. The ellipse represents the 3-sigma uncertainty and is 219 x 73 km (136 x 45.4 mi) in size. The ellipse is centered at 19.45 degrees N and 32.88 degrees W (327.12 degrees E) - that's pretty close to our target of 19.43 deg N and 33.1 deg W (326.9 deg E).
This solution was done on June 23, 1997 for the final design of our 4th maneuver, TCM 4. It put us just outside the blue ellipse at latitude 20.04 degrees N and longitude 31.43 degrees W. Our uncertainties were small enough to display both a "1-sigma" and a "3-sigma" ellipse. The "1-sigma" ellipse represents a 39% change of landing inside the ellipse area while the larger "3-sigma" ellipse represents a 99% chance. The "3-sigma" ellipse is 186 km X 73 km (115.6 x 45.4 mi). TCM 4 was designed to move the center of the red ellipse on top of the red diamond - the target landing site.
For this solution done in May 1997, we were still pretty far away from Mars and our trajectory uncertainty was rather large when mapped to the surface. So I chose to display a "1-sigma" ellipse which (mostly) fits within the bounds of the image and is 227 x 40 km (141 x 25 mi) in size. For the 1-sigma case, we had roughly a 39% chance of landing inside the red ellipse. This ellipse was centered at 20.24 deg N latitude and 33.32 deg W longitude - slightly off the target landing site since TCM 3 did not execute perfectly. Compare this to the latest image above where the current 1- and 3-sigma ellipses are shown. (See the ellipse shrunk and moved around just like I promised!)
This figure illustrates Mars Pathfinder's target landing ellipse projected on a map of southern California. The ellipse is 200 x 100 km in size and is centered on Pasadena (where JPL is located). The ellipse is oriented so that it falls on the land mass of southern California. If oriented at the same angle it takes on Mars, the ellipse would extend out into the Pacific Ocean! Click on the image if you want to see the full-size map showing the entire state.
The map of California used for this illustration was created by Ray Sterner at APL/Johns Hopkins University and is used with his permission. Similar maps for all 50 states can be found in his color landform atlas of the U.S.
Send comments or suggestions to:
Robin Vaughan (firstname.lastname@example.org)
To those of you who have recently sent questions via e-mail, I am working on responses. It may take me a while due to the large volume of e-mail I've received since our landing on July 4th. Please be patient since I do intend to reply to all of your messages eventually. But if you get tired of waiting, check out Mars Team Answers Your Questions and see if you can find your question there.
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