F equals Gravity times the Mass of sun and momentum of planet divided by radius squared


The 2019 Nobel Prize for Physics was awarded yesterday in part to Michel Mayor and Didier Queloz for an amazing discovery they made back in 1995: the first detection of a planet orbiting a far-away star similar to our sun. Before that, the only planets on the map were the eight in our own solar system. We didn’t even know if planets were common or rare in the universe—a question with big implications for the possible existence of alien life.

It was quite a feat of scientific sleuthing. Mayor and Queloz looked at a star in the Pegasus constellation called 51 Pegasi, which is 50.45 light years away. We can see the light given off by the star, but at that distance the angular size of the source is too small for telescopes to resolve. In other words, we can’t really see the star itself. And if you can’t see the star, you certainly can’t see a much smaller planet circling it.

How’d they do it? With physics, of course. As with all things, the best way to understand it is to build a model. So, let’s construct a simple model of the first exoplanet ever detected.

Sifting the Starlight

51 Pegasi is a lot like our sun—a little more massive, but you probably couldn’t tell them apart if they were equally near at hand. The planet, lamely dubbed 51 Pegasi b, is a gas giant like Jupiter, but it’s ridiculously close to its star, with an orbital radius of only about 0.05 AU. (AU stands for astronomical unit, which is the average distance from Earth to the sun.) Just for comparison, Jupiter has an orbital radius of about 5 AU.

Now, I’m going to come at this backwards, with the benefit of hindsight. We’ll use the estimated masses of the star and the exoplanet, along with the orbital radius, to model the behavior of this star-planet system, and then I’ll show how you could detect it. Mayor and Queloz, of course, had to derive those estimates from the data. But they probably had a similar model in mind to guide their work.

OK, in any solar system, there is a gravitational force pulling a star and planet together. This attractive force depends on the mass of each object (Ms and mp) and the distance (r ) between them, and its magnitude is given by:

Illustration: Rhett Allain



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