Astronomers who study pulsars use giant radio telescopes. Pulsars are the remnants of huge supernova explosionsthe results of a giant star running out of nuclear fuel to support it. Stars are giant balancing acts between gravity, which pulls them inward and nuclear explosions, which push them outward. When a giant star (several to a dozen times the Sun's mass or more) runs out of nuclear fuel, its core collapses. The collapse is so jarring that there is a huge explosion, and the material from the star's last reaction spreads through the galaxy. The star becomes brighter than 100 billion normal stars!
This happened about 64,000 years ago in the Large Magellanic Cloud Galaxy, but the light did not reach us until 1987. A more recent explosion occurred about 5,000 years ago. It was closer (in the constellation of Taurus) so the light arrived around 1054 AD (Light travel time requires that one qualify the question "How old is that?" whether the question is for the astronomical object itself or when it was first seen on Earth.)
What is left after these explosions is a neutron stara star so dense that in its constituent atoms the electrons dont have enough room to "orbit" their protons. Consequently, they combine to form neutrons and the star's mass becomes a giant, super-dense neutron star. A tablespoon of neutron star stuff would weight as much as a good-sized mountain range.
Sometimes these neutron stars have huge magnetic fields that direct radio pulses in our direction from one pulse every few seconds up to a thousand pulses per second. We call these "pulsars," and they are extremely interesting star types to study. (The Crab Nebulae pulsar, left from the supernova explosion in Taurus, pulses several times per second.)
Given such a huge, violent explosion of the star (enough to vaporize any planets that might have been there), why would anyone look for planets around a pulsar? Because they might be detected most easily there!
The pulses can be so precisely timed that if the star moved just a bit toward or away from us, the recorded pulses would be altered immediately. Moving a constant pulsar away, for example, would make the received pulse rate slower because each pulse would have farther to travel. The reverse occurs when the pulsar moves toward us. Measuring the radio signals coming from a distant pulsar can help determine whether the star has any orbiting planets.
In 1993 the very first "planets" found around another star system were discovered around a pulsar named PSR B1257+12, pulsing over 1000 times per second (a millisecond pulsar) by an astronomer named Alexander Wolszczan and his collaborators. They discovered two "planets" with masses of 2.8 and 3.4 times that of the Earth! These "planets" are not like the giants found around Sun-like stars today, but more like Earth-mass bodies.
Most theorists think that these "planets" formed after the supernova explosion, but they are nevertheless encouraging signs that planet formation is likely, given the available materials around a star. Who says you can't teach an old star new tricks?