The rotating corpses of massive stars can help scientists weigh the planets in the solar system. By carefully timing radio blips from spinning stellar leftovers called pulsars, astronomers have measured the masses of all the planets from Mercury to Saturn, plus all their moons and rings.

Until now, the only way to figure out the mass of a planet was to send a spacecraft past it. The spacecraft's orbit is determined by the gravitational oomph of the planet (plus whatever moons lay within the spacecraft's orbit), which in turn depends on the planet's mass. The new method is the first to let astronomers weigh planets from the comfort of Earthbound observatories.

"That's what's remarkable about this technique," said space technologist William Folkner of NASA's Jet Propulsion Laboratory, a co-author of a study in the upcoming issue of Astrophysical Journal. "I can't think of any other way to measure masses of planets from the Earth." **

The new method relies on the clock-like regularity of a class of neutron stars called pulsars, the rapidly spinning remains of massive stars that died in supernova explosions. Pulsars shoot tight beams of radio waves into space that sweep across the sky like a lighthouse, so from Earth they appear to blink or pulse.

Because the Earth is always moving around the sun, the time it takes for these radio blips to reach us is always changing. To get rid of this effect, astronomers calculate when the pulse should reach the solar system's center of mass, or barycenter – the point around which all the mass in the solar system moves. But because the planets' arrangement around the sun is constantly changing, the barycenter moves around with respect to the sun, too.

To pin down the center of mass at a given time, astronomers use a special table of where all the planets are, called an ephemeris, plus values for the masses of the planets taken from previous space missions. If the masses are slightly wrong, then a regular, repeating pattern of timing errors appears in the pulsar data. For instance, if Jupiter's mass is a bit off, then an error appears every twelve years, once for every time Jupiter orbits the sun. Correcting the value for Jupiter's mass makes the error disappear.

"You can see that 12 year wiggle in timing of neutron stars," Folkner said. "That tells you how far the sun is from the solar system barycenter, which tells you what the mass of Jupiter is."

An international team of scientists used three different radio telescopes, the 1000-foot-wide Arecibo telescope in Puerto Rico, the 210-foot Parkes telescope in Australia and the 328-foot Effelsberg telescope in Germany to time the blips from four different pulsars over a period of 5 to 22 years. They then used computer models to use the pulsars' times to calculate the masses of Mercury, Venus, Mars, Jupiter and Saturn.

The masses the team found are not as accurate as the best measurements from spacecraft flybys, but they're close. The measurement for Jupiter, for instance, was found to be 0.0009547921 times the mass of the sun. This value is more accurate than the mass determined from the Pioneer and Voyager spacecraft, and less accurate than, but consistent with, the value from the later Galileo spacecraft, which includes more decimal places.

"Our error bars are larger than those of these spacecraft measurements," said study co-author Andrea Lommen of Franklin & Marshall College. "We are admitting freely that you should still use the mass of Jupiter measured from the spacecraft, but it's comforting to know that our measurement agrees with that."

The new method is also the first that can measure the masses of everything in a planetary system, including moons and rings.

"Spacecraft flybys don’t tell us the mass of everything in the Jupiter system, only the parts inside the spacecraft orbit," Folkner said. "With this pulsar timing mechanism, we're sensitive to the entire system, including the moons that are outside the orbit of any spacecraft that have flown by."

The technique is actually a stepping stone to studying something even more exotic: ripples in space-time called gravitational waves that were predicted by Einstein but have never been observed. The timing of pulsar blips should change slightly whenever a gravitational wave goes by, but in order to see these changes, astronomers have to subtract out all the other noise that could alter the pulsar's clock.

This study is "a graphic demonstration that you really have to understand the solar system really well if you're going to be able to confidently detect gravitational radiation," commented astronomer Scott Tremaine of the Institute for Advanced Study in Princeton, New Jersey, who was not involved in the new work. "If they can continue to develop these techniques to the point where they can detect gravitational waves, that will be a dramatically important event."

Image: The sun, Earth and Jupiter orbit a common center of mass. David Champion, MPIfR

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