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22.5: Are There Other Earths?

If by that you mean, are there other planets where we could walk out of a spaceship with no equipment other than a picnic basket, and enjoy a pleasant afternoon on a grassy slope near a stream, then that remains to be seen. On the other hand, if you are asking if other planets exist that are rocky worlds approximately Earth’s size, and orbiting within their star’s habitable zone (the zone in which liquid water, and potentially life, can exist), then many planet hunters are cautiously optimistic that we have found at least 12 such worlds so far.

As of July 2015, NASA’s Kepler mission has detected a total of 4,696 possible exoplanets. The Kepler spacecraft has an instrument to measure the brightness of stars, and looks for tiny variations in brightness that could be caused by a planet passing between the star it orbits and the instrument observing the star. Potential candidates are then examined in more detail to see whether they are in fact planets or not. So far 1,030 of those candidates have been confirmed as planets.[1] Of those, 12 satisfy the criteria of being one to two times the size of Earth, and orbiting their star within the habitable zone.[2]

The uncertainty about the 12 possible Earth-like worlds is related to their composition. We don’t yet know their composition; however, it is tempting to conclude that they are rocky because they are similar in size to Earth. Remember the rules of the accretion game: you can only begin to collect gas once you are a certain size, and how much matter you collect depends on how far away from the Sun you are. Given how large our gas giant and ice giant planets are compared to Earth, and how far away they are from the Sun, we would expect that a planet similar in size to Earth, and a similar distance from its star, should be rocky.

It isn’t quite as simple as that, however. We are finding that the rules to the accretion game can result in planetary systems very different from our own, leading some people to wonder whether those planetary systems are strange, or ours is, and if ours is strange, how strange is it?

Consider that in the Kepler mission’s observations thus far, it is very common to find planetary systems with planets larger than Earth orbiting closer to their star than Mercury does to the Sun. It is rare for planetary systems to have planets as large as Jupiter, and where large planets do exist, they are much closer to their star than Jupiter is to the Sun. To summarize, we need to be cautious about drawing conclusions from our own solar system, just in case we are basing those conclusions on something truly unusual.

On the other hand, the seemingly unique features of our solar system would make planetary systems like ours difficult to spot. Small planets are harder to detect because they block less of a star’s light than larger planets. Larger planets farther from a star are difficult to spot because they don’t go past the star as frequently. For example, Jupiter goes around the Sun once every 12 years, which means that if someone were observing our solar system, they might have to watch for 12 years to see Jupiter go past the Sun once. For Saturn, they might have to watch for 30 years.

So let’s say the habitable-zone exoplanets are terrestrial.

Does that mean we could live there?

The operational definition of “other Earths,” which involves a terrestrial composition, a size constraint of one to two times that of Earth, and location within a star’s habitable zone, does not preclude worlds incapable of supporting life as we know it. By those criteria, Venus is an “other Earth,” albeit right on the edge of the habitable zone for our Sun. Venus is much too hot for us, with a constant surface temperature of 465°C (lead melts at 327°C). Its atmosphere is almost entirely carbon dioxide, and the atmospheric pressure at its surface is 92 times higher than on Earth. Any liquid water on its surface boiled off long ago. Yet the characteristics that make Venus a terrible picnic destination aren’t entirely things we could predict from its distance from the sun. They depend in part on the geochemical evolution of Venus, and at one time Venus might have been a lot more like a youthful Earth. These are the kinds of things we won’t know about until we can look carefully at the atmospheres and compositions of habitable-zone exoplanets.

Exercise 22.2 How Do We Know the Sizes of Exoplanets?

One of the techniques for finding exoplanets is to measure changes in the brightness of a host star as the planet crosses in front of it and blocks some of its light. This diagram shows how the brightness changes over time. The dip in brightness reflects a planet crossing between the star and the instrument observing the star.

Often the planet itself is too small to see directly. If all we know is how the planet affects the brightness of the star, and we can’t even see the planet, then how do we know how big the planet is? The answer is that the two are related. We can write an equation for this relationship using the radius of the planet and the radius of the star.

Plot showing how the star Kepler-452 dims as the planet Kepler-452b moves in front of it. [KP, after Jenkins, J. et al, 2015, Discovery and validation of Kepler-452b: a 1.6REarth super Earth exoplanet in the habitable zone of a G2 star, Astronomical Journal, V 150, DOI 10.1088/0004-6256/150/2/56.]

Decrease in brightness = planet radius squared divided by star radius squared

Let’s try this out for the Earth-like exoplanet called Kepler-452b. The first thing we need to know is the size of the host star Kepler-452. We can get that information by comparing its surface temperature and brightness to that of the sun. Start by calculating the ratios of the sun’s temperature to the star’s temperature, and the star’s luminosity to the sun’s luminosity using the data in Table 22.5.1. Record your answers in the table. Then find the star’s radius using the following equation, and record your result:

star radius = sun radius x (sun temperature divided by star temperature) squared times the square root of star luminosity divided by sun luminosity

 Description Sun Kepler-452 Ratio

Temperature

(degrees Kelvin)

5,778 5,757  

Luminosity

(x 1026 watts)

3.846 4.615  
Radius (km) 696,300    

Table 22.5.1 Calculating the radius of star Kepler-452

The second thing we need to know is how the brightness of Kepler-452 changes as planet Kepler-452b moves in front of it. Use the plot shown in this exercise box to find this information. Find the value on the y-axis where the red curve shows the most dimming from the planet and record your result in Table 22.5.2.

 

Decrease in brightness*

Earth radius

in km

Kepler-452b radius in km Kepler-452b radius/Earth radius
x 10-6 6,378    

Table 22.5.2 Calculating the radius of planet Kepler-452b

* Because we know this is a decrease, you don’t need to keep the negative sign.

Use the following equation to find the radius of Kepler-452b:

planet radius = the square root of star radius squared times decrease in brightness

To put the size of Kepler-452b in perspective, divide its radius by that of Earth and record your answer.

[1] You can access a catalogue of confirmed exoplanets found by NASA and other planet-hunting organizations at http://exoplanet.eu/catalog/

[2] Read more about habitable-zone planets discovered so far at http://www.nasa.gov/jpl/finding-another-earth

* Karla Panchuk, Department of Geological Sciences, University of Saskatchewan

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