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21.4 Planets beyond the solar system: search and discovery  (Page 4/8)

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View a series of animations demonstrating solar system motion and Kepler’s laws, and select animation 1 (Kepler’s laws) from the dropdown playlist. To view an animation demonstrating the radial velocity curve for an exoplanet, select animation 29 (radial velocity curve for an exoplanet) and animation 30 (radial velocity curve for an exoplanet—elliptical orbit) from the dropdown playlist.

Transiting planets

The second method for indirect detection of exoplanets is based not on the motion of the star but on its brightness. When the orbital plane of the planet is tilted or inclined so that it is viewed edge-on, we will see the planet cross in front of the star once per orbit, causing the star to dim slightly; this event is known as transit    . [link] shows a sketch of the transit at three time steps: (1) out of transit, (2) the start of transit, and (3) full transit, along with a sketch of the light curve, which shows the drop in the brightness of the host star. The amount of light blocked—the depth of the transit—depends on the area of the planet (its size) compared to the star. If we can determine the size of the star, the transit method tells us the size of the planet.

Planet transits.

Illustration of a Planet Transits. At the bottom of the figure is a graph. The vertical axis is labeled “Brightness”, in arbitrary units increasing upward, and the horizontal axis is labeled “Time”, in arbitrary units increasing to the right. A curve is plotted showing the brightness of the star as constant. After a time the brightness suddenly drops for a short duration before returning to its original value. At the top of the figure the disk of a star surrounded by an ellipse representing the orbit of a planet is shown. On the ellipse are drawn three dots representing the position of a planet at three different times in its orbit around the star. At position 1 the planet is to the left of the star. A dashed line connects the planet to the plotted curve. At this position the dashed line intersects the curve at a point of constant brightness. At position 2 the planet is just beginning to cross the face of the star. A dashed line connects the planet at position 2 to the curve where the brightness begins to drop. Finally, at position 3, the planet is fully in front of the star and the dashed line from the planet intersects the curve where the brightness is at minimum.
As the planet transits, it blocks out some of the light from the star, causing a temporary dimming in the brightness of the star. The top figure shows three moments during the transit event and the bottom panel shows the corresponding light curve: (1) out of transit, (2) transit ingress, and (3) the full drop in brightness.

The interval between successive transits is the length of the year for that planet, which can be used (again using Kepler’s laws) to find its distance from the star. Larger planets like Jupiter block out more starlight than small earthlike planets, making transits by giant planets easier to detect, even from ground-based observatories. But by going into space, above the distorting effects of Earth’s atmosphere, the transit technique has been extended to exoplanets as small as Mars.

Transit depth

In a transit, the planet’s circular disk blocks the light of the star’s circular disk. The area of a circle is π R 2 . The amount of light the planet blocks, called the transit depth , is then given by

π R 2 planet π R 2 star = R 2 planet R 2 star = ( R planet R star ) 2

Now calculate the transit depth for a star the size of the Sun with a gas giant planet the size of Jupiter.

Solution

The radius of Jupiter is 71,400 km, while the radius of the Sun is 695,700 km. Substituting into the equation, we get ( R planet R star ) 2 = ( 71,400 km 695,700 km ) 2 = 0.01 or 1%, which can easily be detected with the instruments on board the Kepler spacecraft.

Check your learning

What is the transit depth for a star half the size of the Sun with a much smaller planet, like the size of Earth?

Answer:

The radius of Earth is 6371 km. Therefore,
( R planet R star ) 2 = ( 6371 km 695,700 / 2 km ) 2 = ( 6371 km 347,850 km ) 2 = 0.0003 , or significantly less than 1%.

Got questions? Get instant answers now!

The Doppler method allows us to estimate the mass of a planet. If the same object can be studied by both the Doppler and transit techniques, we can measure both the mass and the size of the exoplanet. This is a powerful combination that can be used to derive the average density (mass/volume) of the planet. In 1999, using measurements from ground-based telescopes, the first transiting planet was detected orbiting the star HD 209458. The planet transits its parent star for about 3 hours every 3.5 days as we view it from Earth. Doppler measurements showed that the planet around HD 209458 has about 70% the mass of Jupiter, but its radius is about 35% larger than Jupiter’s. This was the first case where we could determine what an exoplanet was made of—with that mass and radius, HD 209458 must be a gas and liquid world like Jupiter or Saturn.
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Source:  OpenStax, Astronomy. OpenStax CNX. Apr 12, 2017 Download for free at http://cnx.org/content/col11992/1.13
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