1. The Fermi paradox ↑
It seems likely that alien life has evolved somewhere in the Galaxy, given that there may be billions of habitable planets, and many of these may have existed for billions of years. If just one species in the whole of the Galaxy were able to explore using self-replicating spacecraft, then they might be able to place probes across the Galaxy within a million years or so.
There are a number of possible solutions to the Fermi paradox. It may be the case that alien life is not common in any form, it may be the case that intelligent life is not common, or it may be that intelligent species rarely explore space, either due to physical limitations or because they simply don’t want to. It may also be the case that space-faring alien life is common, and we've just not discovered it yet. While there's no way to know the probability associated with each answer, this is certainly possible. If there were a fleet of alien ships at the edge of the Solar System, then we wouldn’t know unless they directly contacted us.
In fact, if an alien spacecraft was headed towards Earth, then there's a good chance that it wouldn’t be detected until it entered the atmosphere, if it's detected at all.
2. Distant objects ↑
The furthest objects to be discovered in the Solar System are in the Kuiper Belt. The Kuiper Belt is a belt of asteroids and comets that orbit the Sun from beyond the orbit of Neptune. It's thought to be composed of over a trillion objects, including hundreds of dwarf planets[6a].
The Solar System. The Kuiper Belt is surrounded by the Oort Cloud, which composed of up to 2000 billion comets. These are too small and far away to be observed with current telescopes and probes. Image credit: NASA/Public domain.
It's possible that we could detect an alien spacecraft in the Kuiper Belt if it happened to pass the field-of-view of one of the telescopes we have in orbit around the Earth, or if it passed close to the New Horizons space probe, but it is very unlikely to do this by accident.
This is because objects in the Kuiper Belt are small and far away, and so it is largely unexplored and unmonitored. We have only observed a few hundred of the 1000 billion objects it's thought to contain, and have only confirmed the discovery of 10 dwarf planets[6b].
If an alien spacecraft did happen to pass the field-of-view of a telescope on Earth, then it would have to be extremely large and extremely luminous for it to be visible from the Kuiper Belt. In order to get a rough idea of its shape, it would have to be comparable in size to Pluto (which is over 2000 km wide, over twice as wide as the second Death Star).
Pluto, image from the Hubble Space Telescope. Image credit: NASA, ESA, H. Weaver (JHU/APL), A. Stern (SwRI), and the HST Pluto Companion Search Team/Public domain.
Pluto, image from New Horizons. Image credit: NASA/JHUAPL/SWRI/Public domain.
3. Near-Earth objects ↑
The probability of detecting an alien spacecraft goes up the closer it gets to the Earth, but it's still very unlikely that it will be detected until it's at least within the orbit of Mars. The asteroid belt between Mars and Jupiter, for example, is thought to contain at least 3 million asteroids, yet only around 700,000 of these have been identified.
Once it passed the orbit of Mars, a spacecraft sized object would be large enough to be detected from Earth. It could then be detected by an amateur astronomer who happened to be looking in the right direction, or in a sky survey such as the Catalina Sky Survey or Pan-STARRS (the Panoramic Survey Telescope and Rapid Response System).
Sky surveys are designed to detect near-Earth objects such as asteroids, comets, and space debris. They work by taking photographs of the sky every night, and then comparing the photos to see if anything has moved relative to the background stars[9a].
Near-Earth objects are objects that come within about 45 million km of the Earth. This is over 100 times the distance to the Moon. There are thought to be about 15,000 near-Earth objects larger than 140 metres in diameter, and about 1000 larger than 1 km[9b]. About 90% of these have been identified[11a].
This leaves about 100 objects over 1 km that have yet to be discovered, and over 1000 smaller objects. Sky Surveys tend to focus on the plane of the Solar System that the planets and asteroids orbit within, and so an alien spacecraft could also evade detection by bypassing this plane completely.
The number of near-Earth asteroids discovered in the last 20 years. Colours indicate the name of the sky survey that discovered them. Image credit: NASA/Alan B. Chamberlin/JPL/Public domain.
An alien spacecraft would be more likely to be detected in a sky survey if it's big and bright. It would also have to be moving slowly enough to be tracked. Asteroids have been detected with speeds of up to 65 km/s[11b], which sounds fast, but this is just 0.02% of the speed of light. At this speed, a journey to the closest star to the Sun would take about 20,000 years.
If an alien spacecraft does travel at the same speed as an asteroid, then it may be detected a few weeks before it arrives at Earth. The faster the spacecraft is, the less likely it is to be identified, and if it travels close to the speed of light, then we would probably not be able to detect it until it arrived.
We might be able to detect an alien spacecraft if it were to decelerate as it approaches Earth. This is because an object cannot decelerate without expelling energy, which we may be able to detect. It may do this with chemical rockets, nuclear power, or solar sails, all of which would produce excess radiation.
4. The Hubble Space Telescope ↑
If an unusual object were detected this close to the Earth, then it may be possible to construct an image of it using the Hubble Space Telescope. Hubble’s Wide Field Camera has a resolution of 0.04’’ (where 1’’=1/3600th of a degree). This means an object that takes up 0.04’’ of the sky would produce 1 pixel in an image produced by Hubble.
In order to take up this much of the sky, an object needs to either be really big, or really close. The full moon, for example, takes up 1800’’ of the sky when viewed from Earth, and Mars takes up about 25’’.
The relationship between an object's angular size and its distance is found using:
Image credit: Helen Klus/CC-NC-SA.
Here d and D must have the same unit (e.g. km), and θ is measured in radians. There are 206,265’’ in 1 radian, and so:
This means that at 642 metres across (about twice the width of the International Space Station), Picard’s Enterprise would not be visible until it was about 3 million km away. This is over 8 times the distance to the Moon, and about 1/36th of the distance to the orbit of Mars.
To discern the shape of an object, it needs to cover enough space to produce more than 1 pixel. To cover a width of 20 pixels, an object would have to take up 0.8’’ of the sky, and to cover a width of 100 pixels, an object would have to take up 4’’ of the sky.
20 pixel wide images of the International Space Station, Comet Churyumov–Gerasimenko, and Pluto. Image credit: modified by Helen Klus, original images by NASA/Public domain, ESA/Rosetta/NAVCAM/CC-A, & NASA/JHUAPL/SWRI/Public domain.
A 20 pixel wide image of Picard’s Enterprise could be made when it is about 165,000 km from Earth. This is just under half the distance to the Moon. For a 100 pixel wide image, it would have to be within 33,000 km of the Earth. This is about 1/12th of the distance to the Moon.
A 20 pixel wide image of the second Death Star, however, would be possible when it is between the orbit of Mars and the asteroid belt, and a 100 pixel wide image would be possible when it is about 45 million km away. This is just within the orbit of Mars. These objects would have to be at least ten times closer to be observed in this detail by a telescope on Earth.
Distance 20px (km)
Distance 100px (km)
International Space Station
Enterprise (Star Trek TOS)
Enterprise (Star Trek TNG)
Borg cube (Star Trek TNG)
Babylon 5 (Babylon 5)
Galactic Empire Executor Class (Star Wars)
First Death Star (Star Wars)
Second Death Star (Return of the Jedi)
The approximate distance in km that an object would have to be for the Hubble Space Telescope to be able to produce 20 and 100 pixel wide images of it. The number in brackets is the distance/the distance to the Moon. Diameters are mostly taken from Spaceship Size Comparison.
The Solar System to scale, showing the distance the first and second Death Stars would have to be from Earth for Hubble to produce a 20 pixel wide image of them.Image credit: modified by Helen Klus, original image by NASA/David Seal/Public domain.
The Earth and Moon to scale, showing the distances Kirk and Picard’s Enterprises’, a Borg Cube, the Babylon 5 space station, and a Galactic Empire Executor Class Star Destroyer would have to be from Earth for the Hubble Space Telescope to produce a 20 pixel wide image of them. Distances from Earth are to scale, the size of objects other than the Earth and Moon are not. Image credit: modified by Helen Klus/CC-NC-SA, original image by NASA/Ernie Wright/Public domain.
5. Entering the atmosphere ↑
Once it entered the atmosphere, an alien spacecraft could be detected over military or commercial airspace using radar, assuming it is not using stealth technology. Although, only a minority of the Earth has radar coverage, and there is no coverage at all over the oceans.
It's quite possible that an alien spacecraft the size of the Enterprise could land on Earth without ever being detected at all.
Surface area of a sphere (s) = 4π × Radius2.
30 AU = 4,487,936,121 km, and so at a radius of 30 AU:
s = 4π × 4,487,936,1212 = 2.53×1020. This is 253 billion billion km2.
θ × D/206,265.
The surface area covered by the Hubble Wide Field Camera is 160×160’’, meaning θ = 160, and so at 30 AU:
160 × 4,487,936,121/206,265= 3,481,297 km.
Area = d2 = 12,000 billion km2.
Area covered by Hubble/Area of sky=
12,000 billion km2/253 billion billion km2= 1/21 million.