Want to Weigh a Star? Use an Alien Planet's Moon

It's always been a challenge for astronomers to record the mass of a star directly, but a new study suggests a novel way to try it — as long as the planets (and moons) align.

The new star-measuring method has promise, but it comes with a lot of 'ifs.'

It only works if the star in question has a planet, and that planet has a moon, and both bodies cross in front of the star.

If all those ingredients are present, then astronomers can use the new method to calculate the star's mass directly by measuring the sizes and orbits of the planet and moon, researchers said. [Illustration: Planet and moon cross in front of star.]

"I often get asked how astronomers weigh stars," David Kipping of the Harvard-Smithsonian Center for Astrophysics said in a statement. "We've just added a new technique to our toolbox for that purpose."

To date, astronomers have found nearly 500 alien planets, more than 90 of which cross in front of — or transit — their stars from our perspective. Astronomers can detect such planets by watching for the dips in a star's brightness that transits cause — a technique known as the "transit method."

By measuring the amount of starlight a planet blocks, astronomers can also calculate how big it is relative to the star. But researchers can't know exactly how big the planet is unless they know the actual size of the star.

How it works

Computer models often give a very good estimate of star sizes, but direct measurements would be best, researchers said.

Kipping realized that if a transiting planet has a moon big enough to be seen from Earth (by also blocking the star's light), then the planet-moon-star system could be measured in a way that allows scientists to calculate exactly how large and massive all three bodies are.

"Basically, we measure the orbits of the planet around the star and the moon around the planet," Kipping said. "Then through Kepler's laws of motion, it's possible to calculate the mass of the star."

Step-by-step process

The process isn't easy, and it requires several steps.

By measuring how the star's light dims when planet and moon transit, astronomers learn three key things: the orbital periods of the moon and planet; the size of their orbits relative to the star; and the size of the planet and moon relative to the star.

Plugging those numbers into Kepler's Third Law — which relates a body's orbital period to its orbital distance — yields the density of the star and the planet. Since density is mass divided by volume, the relative densities and relative sizes give the relative masses.

Finally, scientists measure the star's wobble due to the planet's gravitational tug, known as the radial velocity. Combining the measured velocity with the relative masses, they can calculate the mass of the star directly.

"If there was no moon, this whole exercise would be impossible," Kipping said. "No moon means we can't work out the exact density of the planet, so the whole thing grinds to a halt."

Kipping hasn't put his method into practice yet, since no star is known to have both a planet and moon that transit. However, NASA's planet-hunting Kepler mission could discover several such systems, researchers said.

"When they're found, we'll be ready to weigh them," Kipping said.

This research will appear in the Monthly Notices of the Royal Astronomical Society.

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