Monday, January 14, 2008

The Wobble of Star caused by Hot Jupiter class planets

Hot Jupiters are planets with mass of several Jupiter orbiting as close as Mercury or Venus to their primary star. Planets with such mass orbiting the primary at close distance, may disrupt the movement of the star, causing it to wobble relative to the star’s proper motion.

To show this effect in detail, we will conduct several experiments with a 1.1775 Solar Mass star called Eltera, by placing one or two Hot Jupiters in the system.

Single planet

The first Hot Jupiter we place in this system is a 4.3359 Jupiter Mass planet, called Sivatra. Sivatra is placed in an orbit, 0.3 AU from Eltera, with initial orbital speed of 59.022 km/s (relative to Eltera). The wobble caused by Sivatra is shown below.

The wobble of Eltera caused by single planet orbiting it is relatively simple, by calculating the period of a wobble, we can calculate the period of Sivatra orbit. Then if we know the mass of the star Eltera, we can work out the radius of Sivatra orbit. By analyzing the strength of the wobble and taking the radius of Sivatra orbit, we can derive the mass of Sivatra.

Two planets

Now, how if we add another Hot Jupiter called, Ertina, with mass of 2.7558 Jupiter Mass into the Eltera System ? How the shape of the wobble will be ?

It turns out that depending on the starting position of Ertina relative to Sivatra, the shape of the wobble will be different, but there is a clear clue in the plot result, hinting that there are two planets in the system. The clue is the fact that in all figure above, all plot results shows retrograde movement, with two different period.

By analyzing the time difference per two knots over different time ( with the same method used to examine the plot result of sin(a*t)+sin(b*t) to derive the value of 2*Pi/a and 2*Pi/b ), we can derive the period of each planets. If the mass of Eltera is known, we can later derive the distance of each planets from Eltera, which is the information needed to calculate the mass of each planets.

Download NCGS Program and Source Code here

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