http://marsrovers.jpl.nasa.gov/spotlight/20060302.html
Spirit Discovers “New” Highest Peak in “Columbia Hills”
Jet Propulsion Laboratory
March 02, 2006
Factoid: Hawaii’s Mauna Kea volcano may not seem very tall compared
with Mt. Everest, but if measured from the ocean floor, Mauna Kea would
tower above Earth’s “tallest peak” by a good 4,000 feet (1,220 meters).
Take-home message: Looks can be deceiving.
NASA’s Mars Exploration Rover Spirit has confronted a martian version
of “things being not quite what they seem,” though on a much smaller
scale.
From Spirit’s distant landing site out on the plains of Gusev Crater,
the highest peak in the “Columbia Hills” appeared to be “Husband Hill.”
After making a trek to the “Columbia Hills,” Spirit has been traversing
and studying slopes, rocks, and sand deposits there for more than a
year. New measurements from Spirit show that “McCool Hill” is about 85
feet (26 meters) taller than its neighbor, “Husband Hill.” And, indeed,
digital maps created from orbital images tell a similar story. At
first, “McCool Hill,” partly blocked from view, appeared smaller.
The revised estimates illustrate the importance of location as well as
number of measurements. Generally speaking, the more measurements, the better. Even then, there’s room for error.
For instance, using the 27 Earth-orbiting satellites in the Global
Positioning System (GPS), a team of scientists measured the summit of
Mt. Everest at 29,035 feet (8,850 meters) above sea level ? plus or
minus 7 feet (2 meters), that is.
What’s difficult to pinpoint on Earth is even more challenging on Mars there are only three working orbiters above Mars, and no synchronized
GPS.
Applying Mathematical Logic
Though it may not make any difference to the geologic history of Mars,
some mission team members have an avid interest in knowing which peak
is highest.
“McCool Hill will be a historical landmark for Spirit,” says Dr. Ron
Li, a member of the rover science team as well as a Geographic Information Systems expert and professor at Ohio State University. “She will likely spend the upcoming martian winter there exploring the north-facing slope.”
Knowing more about the characteristics of each hill also holds a
special appeal. To reference the hills in mission planning, team members dubbed each hill in honor of the astronauts from the fallen Columbia space
shuttle.
The first people to suspect a discrepancy in the measurements were
rover engineer Dr. Chris Leger, who climbs mountains in his spare time, and image processing specialist Bob Deen. In panoramic images taken by
Spirit from the summit of “Husband Hill,” they noticed that “McCool
Hill” appeared higher.
Measurements Subject to Improvement
Leger researched elevation angles in images from Spirit’s panoramic
cameras and estimated the peak of “McCool Hill” to be about six-tenths
of a mile (1 kilometer) away and 1.3 degrees higher than the summit of
“Husband Hill.” Using trigonometry, he made a quick calculation that
showed a difference in elevation of 74.2 feet (22.6 meters).
Trigonometry is the branch of mathematics that covers relationships
between the sides and angles of triangles. One of its benefits is that,
if you know the distance to the foot of a mountain and you can measure
the angle between your location and the summit, you can calculate a
mountain’s height.
Li and his team then calculated the actual height of “McCool Hill”
above the surrounding plains based on satellite data. They used the science of photogrammetry (obtaining reliable measurements through photographs) to estimate the hill’s dimensions from stereo (three-dimensional) views taken by the Mars Orbital Camera on the Mars Global Surveyor orbiter.
For measuring the surface dimensions of Earth features, Global
Positioning System satellites use trigonometry too. Two points on the
satellite’s path, together with an unknown point on the planet’s
surface, form the corners of a triangle. After measuring the distance
to the unknown point, it’s possible to pinpoint the precise location of
the unknown point using sines and cosines ? ratios in trigonometry.
Mars Global Surveyor data helped scientists use the same technique. By
comparing orbital measurements of “Husband Hill” to Spirit’s surface
measurements, which are more accurate than measurements from farther
away, Li’s team was able to improve height estimates for “McCool Hill.”
“McCool” Is Taller
Recent measurements from Spirit indicate that “Husband Hill” is 351
feet (107 meters) higher than the point where Spirit landed on the
surrounding plains. Li’s team further estimated “McCool Hill” to be 436
feet (133 meters)–85 feet higher than its neighbor–above Spirit’s
landing site.
Like climbing skills, all measurements are subject to improvement.
Depending on the quality of the data from Spirit and the Mars Global
Surveyor orbiter, the revised height for “McCool Hill” has an estimated
margin of error of about a dozen to a hundred feet (a few meters to a
few tens of meters).
For a hiker with a heavy load, a potential error of 100 feet might seem
significant. For Spirit, it doesn’t much matter as long as the rover’s
solar panels are facing the sun. Still, even though “McCool Hill” and
“Husband Hill” may seem minuscule next to Mt. Everest, they are far and
away the tallest peaks ever climbed by an explorer on Mars.