Teachable Moments| August 17, 2015
'Exoplanets' and the Search for Habitable Worlds
In the News
Twenty years after the first discovery of a planet orbiting another sun-like star, scientists have discovered the most Earth-like exoplanet ever: Kepler-452b. Located in the habitable zone of a star very much like our sun, Kepler-452b is only about 60 percent wider than Earth.
What makes it the most Earth-like exoplanet ever discovered?
First a couple definitions: An exoplanet is simply a planet that orbits another star. And the habitable zone? That’s the area around a star in which water has the potential to be liquid -- not so close to the star that all water would evaporate, and not so far that all water would freeze. Think about Goldilocks eating porridge. The habitable zone is not too hot, and not too cold. It’s just right.
Okay, back to Kepler-452b. Out of more than a thousand exoplanets that NASA’s Kepler spacecraft has detected, only 12 have been found in the habitable zone of their stars and are smaller than twice the size of Earth, making Earth-like planets a rarity. Until this discovery, all of them have orbited stars that are smaller and cooler than our sun.
Kepler-452b is the first to be discovered orbiting a star that is about the same size and temperature as our sun. Not only that, but it orbits at nearly the same distance from its star as Earth does from our sun! Conditions on Kepler-452b could be similar to conditions here on Earth and the light you would feel there would be much like the sunlight you feel here on Earth. Scientists believe that Kepler-452b has been in the habitable zone for around six billion years -- longer than Earth has even existed!
How They Did It
The Kepler spacecraft, named for mathematician and astronomer Johannes Kepler, has been working since 2009 to find distant worlds like Kepler-452b. It does so by looking at more than 100,000 stars near the constellation Cygnus. If one of those stars dims temporarily, it could be that an object passed between the spacecraft and the star. If it dims with a repeatable pattern, there’s a good chance an exoplanet is passing by again and again as it orbits the star. The repeated dimming around one of those stars is what led to the discovery of Kepler-452b.
This exciting discovery provides opportunities for students to practice math skills in upper elementary and middle school, and gives high school students a practical application of Kepler’s third law of planetary motion. Take a look below to see where these might fit into your curriculum.
Upper Elementary and Middle School
After learning about Earth’s cousin, students might wonder about a trip to this world. Scientists have calculated the distance between Earth and Kepler-452b at 1,400 light years. A light year is a measure of distance that shows how far light travels in one year. It’s equal to about 10 trillion kilometers (six trillion miles) or, to be more precise, 9,461,000,000,000 kilometers (5,878,000,000,000 miles). Ask students to calculate the distance between Earth and Kepler-452b at various levels of precision, depending on what they are prepared for or learning. For an added challenge, have them determine how long it would take a fast moving spacecraft like Voyager 1 traveling at 61,000 kph (38,000 mph) to reach this new world.
Note: Due to the approximations of spacecraft speed and light year distance used for these problems in both standard and metric units, there is a variation among the answers.
Distance: 10 trillion km x 1,400 = 14,000 trillion km (that’s 14,000,000,000,000,000 kilometers!)
Travel time: 14,000 trillion km ÷ 61,000 kph ÷ 24 ÷ 365 ≈ 26,000,000 years
Distance: 6 trillion miles x 1,400 = 8,400 trillion miles (that’s 8,400,000,000,000,000 miles!)
Travel time: 8,400 trillion miles ÷ 38,000 mph ÷ 24 ÷ 365 ≈ 25,000,000 years
or more precisely…
Distance: 9,461,000,000,000 km x 1,400 = 13,245,400,000,000,000 km
Travel time: 13,245,400,000,000,000 km ÷ 61,000 kph ÷ 24 ÷ 365 ≈ 25,000,000 years
Distance: 5,878,000,000,000 miles x 1,400 = 8,229,200,000,000,000 miles
Travel time: 8,229,200,000,000,000 miles ÷ 38,000 mph ÷ 24 ÷ 365 ≈ 25,000,000 years
or using exponents and powers of 10…
Distance: 9.461 x 1012 x km x 1.4 x 103 = 1.32454 x 1016 km
Travel time: 1.32454 x 1016 km ÷ 6.1 x 104 kph ÷ 2.4 x 101 ÷ 3.65 x 102 ≈ 2.5 x 107 years
Distance: 5.878 x 1012 miles x 1.4 x 103 = 8.2292 x 1015 miles
Travel time: 8.2292 x 1015 miles ÷ 3.8 x 104 mph ÷ 2.4 x 101 ÷ 3.65 x 102 ≈ 2.5 x 107 years
Middle and High School
The time between detected periods of dimming, the duration of the dimming, and the amount of dimming, combined with a little math, can be used to calculate a great deal of information about an exoplanet, such as the length of its orbital period (year), the distance from its star, and its size.
Kepler-452b has an orbital period of 384.84 days -- very similar to Earth’s 365.25 days. Students can use the orbital period to find the distance from its star in astronomical units. An astronomical unit is the average distance between Earth and our Sun, about 150 million kilometers (93 million miles).
Kepler’s 3rd law states that the square of the orbital period is proportional to the cube of the semi-major axis of an ellipse about the sun. For planets orbiting other stars, we can use R = ∛(T2 ∙ Ms) where R = semi-major axis, T = orbital period in Earth years, and Ms = the mass of the star relative to our sun (the star that Kepler-452b orbits has been measured to be 1.037 times the mass of our sun).
T = 384.84 ÷ 365.25 = 1.05
R = ∛(1.052 ∙ 1.037)
R = ∛1.143 = 1.05 AU
- Exoplanet Travel Bureau Posters
- Video: What’s a “habitable zone?”
- Video: What’s in an Exoplanet Name?
Facts and Figures
TAGS: Exoplanets, Kepler, Kepler-452b, Habitable Zone, Math, Activities, Classroom Activities, Resources