the coin may appear to be smaller, but its
size really hasn’t changed. If a person
knows how large an object appears to be,
and how distant it is, they can work back-
ward to determine the true size of the
object. Simply put, this is also how
astronomers work out the size of distant
objects in outer space.
What “mathematical measurement”
erroronce occurred when a
spacecraft reached Mars?
The Mars Climate Orbiter spacecraft, a
joint effort between Lockheed Martin and
NASA’s Jet Propulsion Laboratory (JPL),
was supposed to go into orbit around the
red planet on September 23, 1999.
Instead, the Martian craft lost all contact with Earth. After much deliberation, a
review panel for the incident came to a disconcerting conclusion: A thruster error
developed when project teams used different measuring systems for the navigation
commands—NASA used metric units; Lockheed Martin used English standard units,
and no one caught the discrepancy.
To this day, scientists can only speculate as to what happened to the orbiter, a craft
sent to study the climate and weather patterns of the Martian atmosphere. Some say
that because the orbiter dropped down to within 36 miles (60 kilometers) of the plan-
et—about 62 miles (100 kilometers) closer than planned—atmospheric friction prob-
ably overheated the propulsion system and tore the vehicle apart. Others believe the
craft was propelled through the atmosphere (or bounced off) and out into space again
and is now perhaps circling the Sun like an artificial comet.
How was math used to discover extrasolar planets?
Astronomers have always dreamed about detecting other planets outside our solar sys-
tem, or “extrasolar planets.” In 1994, Polish astronomer Alekzander Wolszczan (1946–)
announced the discovery of the first extrasolar planet—actually, it was two planets with
masses 3.4 and 2.8 times that of Earth’s mass—orbiting the pulsar PSR B125712. (A
pulsar star sends out a periodic pulse of light detected from Earth.) Wolszczan found
the planets by measuring the periodic variation in the pulse arrival time.
There are several major methods used to search for extrasolar planets, and all of
them entail using mathematics. For example, the Doppler shift method measures the
change in wavelength (color) of light coming from a star over the course of days, months, 293
MATH IN THE PHYSICAL SCIENCES
Using parallax to determine the distance to a star is
done by calculating the apparent shift of a star as the
Earth orbits the Sun.