Tag Archives: orbits

Rings on the TV

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Image: JPL/Cassini

Just a heads-up for those of you who haven’t yet firmed up your television viewing schedules for tomorrow night.

I’ll be appearing in a episode devoted to astrophysical disks (that is, rings) that’s set to air Tuesday night on the History Channel’s Universe series. Time is 9PM/8C. (Not sure when it goes down on the West Coast, “check your local listings”.)

The show delves into the ubiquity of disk-like structures in astrophysics, covering the range of scales from the band of our geosynchronous satellites to the rings of the Jovian planets all the way up to quasars and disk galaxies.

The swarm of satellites and space debris, including the ring of geosynchronous satellites (Source).

To create a visual analogy for Saturn’s rings, we visited a Pizza My Heart in Santa Cruz where they still hand-throw the pizza dough. I lecture about how the elastic forces in the spinning dough play a role similar to a the gravity of the central planet in providing inward centripetal acceleration. All the while, they’re throwing the dough in the background.

Throwing pizza dough to emulate an astrophysical disk.

Later, they got dramatic close-up footage of the spinning disks. There were were several moments when the spinning dough was severed azimuthally, causing the outer edge of the dough to go flying off at a tangent, narrowly missing camera and crew. I ad libbed that this is similar to what would happen with the ring particles if Saturn’s gravity could somehow be cut off.

Tune in to see whether it all bakes up as a credible piece of science popularization…

A look inside an extrasolar planet

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Image Source.

Cranking out a paper invariably takes longer than one expects. Last week, I was confident that Konstantin and Peter and I would have our HAT-P-13 paper out in “a day or so”, and then it ended up taking the whole week. As of ten minutes ago, however, it’s been shipped off to the Astrophysical Journal Letters. It’s also been submitted to astro-ph, hopefully in time to make tomorrow’s mailing.

In the meantime, here’s a link to (1) the .pdf of our text, and (2) the two figures (one, two) both in .gif format. The two figures are 800 pixels across, all the better for dropping in to presentations.

Put briefly, HAT-P-13 is an absolutely remarkable set-up. The presence of the outer perturbing body in its well-defined orbit allowed us to show that the system has undergone long-term evolution to a “tidal fixed point”. In this state of affairs, secular variations in the orbital elements of the two planets have been damped out by tidal dissipation, the apsidal lines of the orbits have been brought into alignment, and most importantly, the two orbits precess at the same rate. The paper shows how the eccentricity of the inner planet is a sensitive function of the planet’s interior structure, and in particular, the degree of central concentration (parameterized by the “Tidal Love Number”, k_2).

Here’s a schematic that shows what’s going on:

Right now, the eccentricity of the inner planet is determined to rather modest precision e=0.021 +/- 0.009. The system is transiting, however, and so when Warm Spitzer measures the secondary eclipse time, the error on the eccentricity measurement will drop dramatically. The situation will also benefit from an improved measurement of the planet’s radius. When improved measurements come in, it’ll be possible to literally read off the planet’s core mass and, in addition, the value of the much-discussed tidal quality factor Q.

Lucky 13

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In reviewing grant proposals and observing proposals that seek to study extrasolar planets, one notices that two cliches turn up with alarm-clock regularity. Number one is Rosetta Stone, as in this or that planetary system is a Rosetta Stone that will enable astronomers to obtain a better understanding of the formation and evolution of planetary systems. Number two is ideal laboratory, as in this or that system is an ideal laboratory for studying the processes that guide the formation and evolution of planetary systems.

A terse unsolicited e-mail from Gaspar Bakos always means that a big discovery is in the offing, and today was no exception:

Hello Greg,

You may like this.
http://xxx.lanl.gov/abs/0907.3525

Best wishes
Gaspar

Indeed! HAT-P-13b and c constitute a really exciting discovery. For a number of reasons, this system is a Rosetta Stone among extrasolar planets, and in large part, this is because the system is an ideal laboratory for studying processes such as tidal dissipation and orbital evolution.

HAT-P-13 harbors the first transiting planet that has a well-characterized companion planet. In this case, the outer companion has a P=428 day orbit, an Msin(i) of 15 Jupiter masses, and an eccentricity, e=0.7. In the following diagram, the orbits and the star are shown to scale; the small filled circles that delineate the outer orbit show the position of the outer planet at 4.28 day intervals.

Illustrator-editable PDF of the above

Of obvious interest is the question of whether planet c can be observed in transit. The a-priori probability is seemingly enhanced by the transit of the inner planet. (Give that one to the good Reverend Bayes). The next opporunity rolls around in April 2010, with the opportunity to observe secondary transit following a bit more than two months later.

It’ll be quite something if planet “c” does transit. A sense of the wide open spaces in the system can be obtained by plotting the star and the two planets to scale with their respective separations at the moment of inferior conjunction. Given the width restriction of the blog post format, one needs to present this plot vertically:

There’s a lot more to say about the HAT-P-13 system — so much in fact, that Peter Bodenheimer, Konstantin Batygin and I are furiously writing an ApJ letter. Should have it out the door in a day or so, with a roundup to follow here on oklo.org immediately thereafter…

Glass 99% full

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A little over a year ago, I wrote two posts (one, two) that described (then) undergraduate student Konstantin Batygin’s work on the classical problem of the dynamical stability of the solar system. Konstantin and I were amazed to discover that the inner planets can be destabilized within the next 5 billion years by a linear secular resonance that brings Mercury’s orbital precession into sync with Jupiter’s — a state of affairs that’s akin to firing the starting gun at a Figure 8 race:

And it wasn’t only Mercury that ran into problems. At t=822 million years, shortly after Mercury’s entrance into a zone of severe chaos, Mars — rovers and all — was summarily ejected from the Solar System.

Just after we submitted our paper to the Astrophysical Journal, we learned that we’d been scooped by LeVerrier’s heir in Paris, Jacques Laskar, who had independently submitted a paper drawing essentially the same conclusions to Icarus.

The papers from last year did not include the effect of general relativistic precession. It seemed prudent to first tackle the classical N-body problem. Ironically, the fact that Mercury’s precession is sped up by General Relativity provides a very significant improvement in the stability of the solar system — “Einstein saves the day.”

A paper in this week’s issue of Nature by Laskar and computer engineer Mickael Gastineu brings effective finality. Laskar and Gastineu used the JADE supercomputer at the French National Computing Center to integrate a staggering 2,501 orbital solutions of the full solar system, each of 5 billion year duration. The integrations include general relativity, the gravitational effect of the Earth-Moon binary, and use an ultra-precise ephemeris. They make millimetric changes to Mercury’s orbit and take advantage of the butterfly effect to gain a statistical assessment of the solar system’s prospects.

And the final answer?

There’s a 1% chance that Mercury’s orbit will be destabilized within the next 5 Billion years. It’s possible (although considerably less likely) that Earth can take a direct hit from Mars as a result of Mercury’s transgressions. The paper makes dramatic reading.

Dramatic enough, in fact, that for the past day and a half, I’ve taken a ride on Laskar and Gastineau’s disaster movie-ready coat tails. I wrote the accompanying News and Views article, which has been nosing into the media alongside their results, and I’ll be talking about orbital dynamics, the history of the few-body problem and planetary collisions later today on NPR’s Science Friday. Listen in if you’d like, or check out the podcast when it comes out.

What’s your angle?

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P. Diddy flossing his '606 pose.
Happy ‘606 day!

HD 80606b swung through periastron at about 01:40 UT this morning (Feb. 8, 2009) and will spend the balance of the week spinning out toward inferior conjunction, which will occur at 00:50 UT on Valentine’s day (Feb. 14th).

Proposals for GO-6, the first general observing cycle of the forthcoming Spitzer Warm Mission, were due on Friday. Jonathan and Drake and I worked right down to the 5 PM PST wire, polishing our request to complement the Nov. 2007 8-micron periastron observations with a pair of additional photometric time series at 4.5 microns (Warm Spitzer’s longest IR wavelength). Two HD 80606b events are observable during GO-6; the first at the very start of the warm mission on May 30, 2009, and the second on Jan 08, 2010. We’re keen to watch the planet ring down from its maximum brightness, so we’ve proposed for a window that runs from 10 hours before periastron to 30 hours after periastron. In the 4.5 micron bandpass, we’re predicting a maximum planet-to-star flux ratio of a bit more than one part in a thousand — easily within Spitzer’s sensitivity.

Here’s a diagram showing the portion of the orbit that we’re proposing to observe. Even though the orbital period is 111.43 days, our forty-hour proposed observation encompasses more than 200 degrees of true anomaly. A planet with e=0.932 is quite truly anomalous.

In the near term, though, I’m very eager to see what shows up in my inbox on Valentine’s day, when observers across the Northern Hemisphere will be monitoring HD 80606 to ascertain whether a primary transit for the planet can be observed.

Here’s the geometric situation. If HD 80606’s orbit were inclined only negligibly to the sky plane, then Earth’s view of the system would be a simple reflection of the standard diagram. At inferior conjunction, six days after periastron, the planet is heading away from the star and slightly toward Earth:

The occurrence of the secondary transit tells us, however, that the orbital inclination relative to the sky plane is in reality close to 90 degrees. Using the Illustrator scale tool to compress along the north-south direction, we can see the result of increasing the inclination.


“Sooner can a camel thread the eye of a needle…”