In July 2015, NASA announced that its Kepler space telescope had discovered an Earth-like exoplanet, Kepler 452b; Earth-like because it was in the habitable zone around its star, not too hot and not too cold so water might be found there. This star/exoplanet system is estimated to be 1400 light years away, so how was it found ?! When we are looking for exoplanets, what methods are we using and how accurate does the data have to be? The way I have tried to answer those questions was to ask a rather different one. Could technologically-advanced aliens find the Earth with the methods we currently use in our exploration ? The following is based on some very simplistic calculations estimating the effects that our inquisitive aliens might have to detect if they were to locate us. To my pleasant surprise when I then googled some information to check on a few points, the values I had estimated were corroborated there (see links at the end).
“Discovering us” using perturbations of the Sun
The aliens might try to find us by looking at small perturbations in the position and movement of the Sun. This is a theoretical possibility because it is not correct to say that a planet orbits a stationary star. Both will be orbiting a point called the barycentre, effectively the centre of mass of the two objects , the location of which is decided by their relative masses. For two objects of equal mass, the barycentre will be half way between them. If they are of unequal mass, the barycentre will be shifted towards the heavier object. The Sun is 333,000 times more massive than the Earth which means the barycentre will be very close to the actual centre of the Sun. The Sun-Earth distance is about 150millionkm so using simple proportion the barycentre is about 450km away from the centre of the Sun. This means that the Sun makes a gentle orbit around that point once a year.
The slow orbit of the Sun gives two effects. One of them is that the Sun will wobble slightly, very slightly, changing its position by 900km, just 0.06% of its radius. The orbit will also give a slight Doppler shift to the light coming from it. At some parts of its orbit, the Sun will be moving away from our aliens giving a slight red shift. At other times, it will be moving towards them giving a slight blue shift. The Sun’s yearly orbital journey because of the Earth’s presence is roughly 2900 km which means the speed is 10cm/second. This is called its radial velocity. HARPS, the High Accuracy Radial Velocity Planet Searcher based in Chile claims to detect the shift in line spectra caused by a radial velocity of 20 – 30 cm/second. So maybe if our aliens had a slightly better instrument they could pick up such tiny variations.
The main problem for our aliens trying to detect us using the motion of the Sun is the presence of Jupiter. The radial velocity method and/or wobble method can work for a one planet system, particularly if that is a large planet relatively close to its star. Such a planet is usually referred as a Hot Jupiter. It cannot be not that easy to analyse where there are several planets in the system. The effect of Jupiter’s gravitational field on the Sun would probably swamp any perturbation that the Earth could produce. It seems very unlikely that the Earth could be distinguished by observing the motion of the Sun
Spotting a transit
A better approach for detecting Earth is the transit method which is in fact the one used by the Kepler space telescope. As a planet orbits its star, it is possible for the star, planet and observer to be exactly aligned for a brief portion of the orbit. During the transit, a small part of the star’s light is blocked by the planet and there is a corresponding drop in the overall intensity reaching an observer. This is what the Kepler space telescope looks for and it seems to me to be the most likely way for aliens to find us. How long would the transit last? The Sun’s angular diameter is about ½ a degree, 1/720th of the Earth’s orbit. The Earth would therefore take about half a day to complete its transit, assuming it went across the Sun’s diameter. The transit could be observed once a year. Several such transits would be needed before the aliens could confidently conclude the reduction in intensity was due to a planet passing the star.
And now the key question : how much reduction in intensity would occur during a transit? The radius of the Sun is 109 times greater than that of the Earth, but let’s call that 100 times. So the cross-sectional area of the Sun is 10,000 times greater than that of Earth’s. If the aliens could see the Earth in transit, they would see a black dot covering 1/10000 of the Sun’s disc. The intensity will therefore drop by 1/10000 ie 0.01% (Both Earth and Sun would be very far away from the aliens so I don’t need to take into account the effect we have with the Moon – it appears large because it is much nearer to us than the Sun).
The real problem with the transit method is that the Sun, Earth and the observer must be correctly aligned. If you imagine the Sun at the centre of a sphere with radius equal to that of the Earth’s orbit, then the observer could be anywhere “outside” this sphere. There will only be an observable transit if the observer is actually in line with a band around this sphere, the height of which is equal to the Earth’s diameter. This represents just 0.43% of the sphere’s surface area so it is highly improbable that the observer would be in the right position.
All the effects I’ve described are tiny and it seems impossible that they could be effective ways of identifying a planet – and I haven’t included any limitations about the distance between observer and planet. The further away a star is the fainter it will be and the greater the problem in picking up a 0.01% reduction in intensity. And yet … the Kepler space telescope has managed to identify Kepler 452b where the detection issues would be largely comparable. Wow, what an achievement!
Maybe there are aliens out there somewhere looking for habitable planets. If they were correctly aligned with the Earth-Sun system, and if there was no other object in the way, and if they were looking in our direction at the right time to detect the 12 hour transit, and if they were near enough to detect the tiny drop in intensity, and if they noticed this happening once a year, then they could conclude that the Earth existed … but I won’t be expecting a visit any time soon.
Footnote : I estimated the values given in this article such as the Earth’s radial velocity in a very simple way, eg using round figure values and taking the Earth’s orbit to be circular. I have since found calculations of this data on the following websites and was pleasantly surprised to see that my values were reasonably close to those ones.
https://en.wikipedia.org/wiki/Doppler_spectroscopy gives the radial velocity of the Sun due to the Earth as 0.09m/s, ie 9cm/s
https://en.wikipedia.org/wiki/Kepler_(spacecraft) gives the reduction of intensity of the Earth transiting the Sun as 0.01% and it gives the probability of correct alignment to observe such a transit as 0.47%.
My values were 10cm/s for radial velocity, 0.01% for the reduction in intensity and 0.43% for the probability of correct alignment. Not an exact match for all three but I’m happy with that level of agreement!
By Katherine Rusbridge
Aug 2015