How it’s done
The factors discussed previously can be expressed mathematically and combined to work out the probability that a particular type of planet orbiting a particular type of star will be detected by Kepler. For a very close-in large planet orbiting a particular type of bright star, the probability might be, say, a one-in-four chance. This could also be expressed as a probability of 0.25 or 25%. Imagine Kepler studied, say, 1000 stars of exactly this type and found five such close-in large planets. A probability of 0.25 means that for every planet detected, there are probably another three which exist but are not detected – we detect only a quarter of the planets of this particular type. So, the five planets which were detected should be multiplied by a factor of four to give our best estimate of the number of such planets which actually exist. In this case, we would estimate that there are 20 of these close-in large planets orbiting the 1000 stars studied.
We can take this one step further. Say the Galaxy contains N stars (where N is a big number) of the same type as the sample of 1000 studied. We can use our estimate from the Kepler detections to calculate the total number of close-in large planets orbiting this type of star. We worked out that there are 20 close-in planets orbiting around 1000 such stars, so there are on average 20/1000 (two in every hundred) close-in planets for each star of this type. We then multiply this by the total number of such stars, N. The answer, 20/1000 × N = 0.02 × N, will be the number of close-in planets which exist in orbit around this type of star in the Galaxy.
Activity _unit7.2.2 Activity 2 Planets around F-type stars
Let’s imagine that, out of 1000 F-type stars studied, Kepler found two planets with radii between eight and 16 times the radius of Earth, with orbital periods of less than 50 days. The probability that Kepler will detect such planets is calculated to be one-in-five, that is, 0.2 or 20%. The whole Galaxy contains 3 billion F-type stars.
Work out how many planets with radii between eight and 16 times the Earth’s radius, orbit F-type stars in our Galaxy with orbital periods of less than 50 days.
Answer: 30 000 000 or 30 million
Kepler found two planets per 1000 F-type stars of the kind we are interested in, and had a one-in-five chance of doing so. This means that there is likely to be a factor of five times as many such planets than were actually detected, giving ten planets per 1000 stars, or one planet per 100 stars. So, the number of planets of this type is one per cent of the number of stars. As there are a total of 3 billion F-type stars in the Galaxy we need to find one per cent of 3 billion. This is 3000 000 000 ÷ 100 = 30 000 000.
So, the numbers given suggest there are 30 million planets in the Galaxy with orbital periods of less than 50 days and radii between eight and 16 times the Earth’s radius orbiting F-type stars.
Note that this is just an example of how these calculations work: the numbers are invented!
The same logic can be applied to every combination of type of star and type of planet. Adding up all the estimates for the number of planets of each type gives an estimate of the total number of planets in the Galaxy.