Exoplanets

A new feature in the Exoplanethunter android app is that the planets of our solar system and the Moon has been added to the star map. By using the phone's sensor (GPS sign) it is possible to pinpoint the objects on the night sky

So how is it possible to locate the planets and the moon in the sky. Here are a short mathematical explanation and a historical background to the theory.
Claudius Ptolemy was a Greek astronomer born around 90 and died around 170. He lived in the city of Alexandria in Egypt that was a Roman province at the time. He summarized and extended the ancient astronomical knowledge. He is known for the Ptolemaic system that was based on the ancient belief that the Earth was in the center of the universe and that the Sun, Moon, stars, and planets orbited Earth. A model that also was his predecessor Aristotle (384 BC-322 BC) position.  A problem with the Geocentric model was to explain the weird movement of the planets. Ptolemy described the movements of the planets with epicycles. It means that the planet was moving in a circle and the center point on that circle was moved along the periphery on another circle with Earth near at center. Ptolemy introduced the concept of equant. It was the point from which the movement looked uniform. The equant was inside the circle and directly opposite to Earth from the center of the circle. The Ptolemaic system was the dominating astronomical system during antiquity and middle ages. The first astronomy book based on a heliocentric worldview was the Revolutions of the Heavenly Spheres. The book was written by the Polish astronomer Nicolaus Copernicus but was first published shortly before his death in 1543. In his model, Earth and the other planets were orbiting the Sun and that explained the weird movements of the planets. This theory was later supported by Galileo Galilei's work and the church banned the book.

The astronomer and mathematician Johannes Kepler studied the movement of the planet and made accurate calculations. He formulated three scientific laws that describe the motion of planets around the Sun. It was published between 1609 and 1619 and improved Copernicus heliocentric theory. These laws also laid the ground to Isaac Newton's laws of gravity.

Kepler's three laws are the following:

1. The orbit of a planet is an ellipse with the Sun at one of the two foci.
2. A radius vector joining any planet to the Sun sweeps out equal areas in equal lengths of time.
3. The expression \(\frac {T ^ {2}} {r ^ {3}}\) gives the same constant value for all planets that orbit the Sun, where T is the planet's orbit period and r is half the major axis of the ellipse.

To calculate the position of the planets on the sky seven steps are needed. A celestial object has coordinates right ascension and declination. These coordinates are fixed points with reference origo where the earth's celestial equator is crossed by the ecliptic line. How these coordinates could be calculated from a position on earth can be found here: How do locate stars

Step 1: Calculate the mean anomaly. The mean anomaly is the angular distance from the point where the planet was closest to the Sun (perihelion) which the planet would have moved if it had a circular orbit and with the same orbital period as the real planet moving on the ellipse. If we use a reference point in time where we know the value of the mean anomaly

$$M=M_{o}+\sqrt[]{\frac{\mu}{a^{3}}}(t-t_{0})$$

where a is the length of the semimajor axis of the orbit and \(\mu\) is the mean angular motion  of the object

Step 2: calculate the true anomaly. The true anomaly is the real angle between the perihelion and the planet, seen from the sun and measured in the direction of movement of the planet. The true anomaly can be calculated from the mean anomaly by using a Fourier expansion

$$\nu =M+\left(2e-{\tfrac {1}{4}}e^{3}\right)\sin {M}+$$

$${\tfrac {5}{4}}e^{2}\sin {2M}+$$

$${\tfrac {13}{12}}e^{3}\sin {3M}+....$$

Step 3: calculate the distance from the sun. Eccentricity measure how an orbit deviates from circular by using the value of the planet eccentricity the distance from the sun could be calculated using this formula

$$r=\frac{a(1-e^{2})}{1+e\cos \nu }$$

Where e is the eccentricity

Step 4: calculate the rectangular heliocentric ecliptic coordinates these coordinates is

$$x= r(\cos\Omega\cos(\omega+\upsilon)-$$$$i\sin\Omega\sin(\omega+\upsilon))$$

$$y= r(\sin\Omega\cos(\omega+\upsilon)+$$$$\cos i\cos\Omega\sin(\omega+\upsilon))$$

$$z= r(\sin i\sin(\omega+\upsilon))$$

i is the inclination the angle between a plane of reference and the orbit of the planet. \(\omega\) is the angle between the periapsis (the closest distance from the sun) and its ascending node. \(\Omega\) is the ecliptic longitude. These four steps need to be done for both the Earth and the planet we are investigating

Step 5: calculate the coordinates of the planet relative to the Earth

$$x=x_{planet}-x_{earth}$$

$$y=y_{planet}-y_{earth}$$

$$z=z_{planet}-z_{earth}$$

Step 6 calculate the geocentric ecliptical longitude and latitude by using the coordinates in step 5.

$$\lambda = \arctan (y,x)$$

$$\beta =\arcsin\left (\frac{z}{\sqrt{x^{2}+{y^2}+z^{2}}}\right)$$

Step 6  Earth's tilt angle with respect to the ecliptic line (Earth's path around the sun) is called obliquity of the ecliptic \(\epsilon\). By using \(\lambda\) and \(\beta\) we can now calculate the right ascension \(\alpha\) and declination \(\delta\) of the planet with these formulas.

$$\delta = \arcsin(\sin\beta\cos\epsilon +$$$$ \cos\beta \sin\epsilon\sin\lambda)$$

$$\alpha = \arctan(\sin\lambda\cos\epsilon-$$$$\tan\beta\sin\epsilon\cos\lambda) $$

The moon's position need to be calculated in a different  way as it revolves around Earth.

Geocentric ecliptical coordinates  that were calculated in step 6 for planets could be calculated for the Moon using these formulas:

$$\lambda = L +6.289\sin M$$

$$\beta =5.128\sin F$$

Where L is the mean geocentric ecliptic longitude M mean anomaly and F mean distance   

More details and example calculations can be found here aa.quae.nl

Life on Mars is a song by David Bowie from 1971 on the album Hunky Dory it was also released as a single. But David Bowie was not the first one considering it could be life on Mars. The past 300 years people have believed it could be life on Mars. Christiaan Huygens was a Dutch astronomer that is known for the discovery of Saturn rings he also studied Mars with a telescope.
He discovered a dark spot on the planet known as Syrtis Major and included it in a drawing of Mars in 1659. He used repeated observations of the feature to estimate the length of a day on Mars and that happens to be 24 hours the same as Earth. We know now that the dark color comes from the basaltic volcanic rock and the lack of dust. He also estimated that Mars is about 60 percent of the size of Earth. In 1672 he makes a drawing of Mars that includes the south polar cap.

Later Sir William Herschel that is also known for discovering Uranus in 1780 was studying Mars. He believed that the dark areas on Mars were oceans and the lighter regions land. He speculated that Martian inhabitants have the same climate and conditions as people on Earth.
The famous mathematician Friedrich Gauss was so convinced that intelligent life existed on Mars that he proposed that we should draw huge figures in the snow to signal the Martians.
In 1877, astronomer Giovanni Schiaparelli saw several lines crossing each other on the Martian surface. He believed this was canals built by the Martians to lead water from the polar regions. Percival Lawrence Lowell fueled speculation that there were canals on Mars. The belief of Martians inspired H.G Wells to write the book “The War of the Worlds” that was published in 1897.

The Mariner Program was a series of teen NASA built interplanetary space probes that were sent to several planets in our solar system Venus, Mercury, and Mars. Mariner 4 made the first successful Mars passage in 1965 and sent pictures on the Mars surface. Both Mariner 6 and 7 passed Mars in 1969 and sent data and pictures back to Earth. Mariner 9 became the first artificial satellite in orbit around Mars in 1971. There was no sign of canals. The canals Giovanni saw was just an optical illusion. The Mariner saw indications that there could have been water on Mars in the past. These evidence on ancient water on Mars was not entirely confirmed by the Mariner mission and a closer look was needed. 

The Viking 1 lander was the first spacecraft ever to land successfully on Mars on July 20, 1976. Two months later, the Viking 2 lander landed on Mars. The landers took images of the surface and studied soil samples for biosignatures and one of the tests was positive. But the result could not be reproduced and the positive test was probably the result of a non-biological reaction.

When I was young in 1996 I heard the sensational news on television that the scientist finally found evidence on life on Mars. A billions years old Martian meteorite that was found in Antarctica contained alien bacterias. But this was probably also a false alarm. These features on the Martian meteorite could also be the result of non-biological chemical reactions.

The spacecraft Odyssey Orbiter reached Mars on October 24, 2001, and its scientific mission began on February 19, 2002. Its three main measure instruments were a thermal emission imaging system, a gamma-ray spectrometer, and an energetic particle spectrometer. In addition to these, a neutron spectrometer was also included. The Orbiter found a large amount of hydrogen, a sign that water exists less than one meter below the surface. Two rovers named Opportunity and Spirit were sent to Mars to investigate. Opportunity landed in Meridiani Planum on January 25, 2004, Spirit landed on the other side of the planet three weeks later. Spirit got stuck in a sand trap in 2010. Opportunity continued being operational and last heard of in June 2018. After a planet-wide storm NASA was hoping that it would come back online but it never did. Both rovers found geological evidence that Mars used to be more liquid having oceans. Phoenix lander was the first vessel to investigate Martian water in the Northern polar region. It found perchlorate in the water it is salt that acts like antifreeze and that could be bad news for life.

Image credit: NASA/JPL-Caltech/MSSS

The latest rover Curiosity landed on Mars 5 August 2012. The rover is still operational and confirmed the presence of water in the soil. Recent studies show methane in the atmosphere and organic molecules on the surface. These could still be the result of non-biological processes but it got the scientists very excited as it could come from the decay of once living matter. One of the recent discoveries is that it is a 20 km wide underground lake on Mars. Curiosity will continue its mission until 2020, but more missions are planned. ExoMars is a project to search for signs of past life on Mars and is run by the European Space Agency (ESA) and the Russian space agency Roscosmos. They are planning to land the Rosalind Franklin rover on Mars on July 2020.

Finding evidence on past life on Mars will tell us that if the conditions are right on a planet life will evolve. So far we only know one place in the universe where life developed, on Earth. If it happened twice in our solar system then it probably will be life on Exoplanets that have similar conditions as us.

Visit Mars in the catalog here
 

Kepler telescope was launched by NASA on 7 mars 2009 to monitoring a large number of stars in the constellations Cygnus, Lyra, and Draco. The telescope was placed in orbit around the sun. The main goal was to look for planets that were similar to Earth. The ideal Earth 2.0 will have the same size as Earth and orbiting a Sun similar as our and is in the so-called Goldilocks zone of its star, those planets could harbor life if the planet has the correct atmospheric conditions and liquid water. The thought was also by monitoring approximately 100 000 stars we will be able to get statistics on how many Earth-similar planets that orbit sun-like stars it is in our galaxy.

Kepler-22 is a star in the northern constellation of Cygnus 600 light years away. It is a sun-like G-type main-sequence star a so-called yellow dwarf. Kepler 22 is just is slightly smaller and cooler than our Sun. The first transit of a planet orbiting Kepler 22 was observed already on the third day after Kepler's service begun on 12 mars 2009. The third transit was observed on 15 December 2010. These measurements were confirmed by observations made by the Spitzer telescope and from Earth-based telescopes. On 5 December 2011, the announcement about the first potentially habitable exoplanet has been discovered was released.   

Kepler 22 b is more than twice the size of Earth it has a radius of 2.35 times Earth's radius and 20 times more massive. As gravity is proportional to the mass of the planet divided with radius squared.

$$ g\propto \frac{1}{r^{2}}\Rightarrow \frac{20.36}{2.35^{2}}  =3.68  $$

It will have about 3.6 times the gravity than Earth. Kepler 22 b has a similar orbit as Earth a year on Kepler 22 b, is 290 days long. Kepler 22 b is a so-called Super Earth. It could have oceans but it could have an environment that is closer to Neptune.  

Image credit: NASA/Ames/JPL-Caltech

The first-ever exoplanet found around a G2V star as our sun and at the same distance from its star as Earth is Kepler-452b. The planet is often quoted Earth 2.0 or Earth’s cousin. It is 1.63 times larger in radius than Earth and is 4.7 times more massive than Earth. The planet is a Super-earth. There are also indications that the planet has water on the surface, which increase the possibility of life. A year on Kepler-452b is 380 days long just 15 days longer than Earth. The planet is about 1,400 light-years away from the Solar System. The star 1.4 billion years older than the Sun so the aliens there should have a much longer time than us to evolve their civilization. As the planet has twice the gravity than Earth the aliens would be twice as strong as we are.

$$ g\propto \frac{1}{r^{2}}\Rightarrow \frac{4.7}{1.63^{2}}  =1.77$$

The planet was discovered on 23 July in 2015 by the Kepler telescope.

The closest star that has exoplanets and that is similar to our own Sun (G-type star) is called Tau Ceti it is only just 12 light years away. Tau Ceti mass is 78 percent of our Sun. Tau Ceti has 7 confirmed exoplanets. Tau Ceti e is on the inner border to the habitable zone where it might be too hot and Tau Ceti f is on the outer border to the habitable zone where it might be too cold, but it is still a very interesting object with high Earth similarity index.

The farthest potentially habitable exoplanet discovered is Kepler-1638 b at approximately 2,900 light-years from Earth and it orbits a G-type star. With similar size and age as our Sun. Kepler-1638 b has a mass 8 times earth and its radius is 1.87 times Earth radius and 2.26 times the gravity

$$ \frac{8}{1.87^{2}}  =2.28$$

it was discovered in 2016. Two similar planets were also discovered the same year Kepler-1606 b and Kepler-1090 b

These are all the potentially habitable planets that been discovered around G-type stars so far and Kepler-452 b is the most Earth-like planet discovered yet. Planets that have the same size as Earth has been discovered around red dwarfs stars, but those stars could have dangerous for life radiation and their planets have tidally locked orbits. The new space telescope TESS will now continue the search for Earth 2.0 now when the Kepler telescope has retired.

Arecibo Observatory in Puerto Rico is a very large radio telescope build inside an abandoned sinkhole in May 2017 the telescope was looking for exoplanets around red dwarfs. A red dwarf is much smaller than our Sun and small earth size objects are easier to spot around small dim stars. These are so-called quiet stars its ultraviolet radiation would not strap the potential orbiting exoplanets from its life-supporting atmosphere. The stars that were examined was Ross 128, Gliese 398, Gliese 436, Wolf 359, HD 95735, BD +202465, and K2-18). The telescope detected a new kind of signal never seen before from Ross 128, 11 light-years from Earth. The signal lasted for around 10 min and was in frequencies between 4.6 and 4.8 GHz. The uniqueness of this signal gave rise to some speculation it could be alien in origin.

The Arecibo scientists worked with researchers from the SETI Institute reach and ruled out that the signal is from an alien civilization. It was probably coming from our own satellites It would explain why the signals have the same frequencies interval as our satellites, and Ross 128 was close to the celestial equator where many of the satellites are stationed. Astronomers call this the Weird! signal in honor of the Wow! signal from 1977 that still remains as one of the strongest candidates for alien transmission. The PHL also conducted a survey with almost 800 participants to find out what people thought was causing the Weird! Signal. The Weird! Signal was never heard of again.

Here is the press release at PHL about the Weird! Signal /press-releases/theweirdsignal  

Credit: ESO/M. Kornmesser

An exoplanet orbiting Ross 128 was discovered in July 2017 by the HARPS instrument at the La Silla Observatory in Chile using the radial velocity method. Its existence was confirmed on 15 November 2017 and was given the name Ross 128 b. The planet is in the habitable zone of its star in the so-called Goldilocks zone. Ross 128 b is one the best candidate for a potentially habitable exoplanet confirmed so far. It has the mass 1.35 of Earth. If it has an atmosphere and if it has the right chemical balance for life it could be an earth 2.0. That is not proven it could have the same condition as Venus depending on the greenhouse effect. Ross 128 b is just like Trappist-1 planets and Proxima b tidally locked in its orbit around the star. Eternal night on one side and eternal day on one side. Its year is only 9.9 days long. As Ross 128 is twice the age of our Sun the potential aliens of that planet would have billions of years more than us to evolve their civilization.

Visit Ross 128 b here: Ross 128 

Titan that is the largest moon of Saturn is the only moon in our solar system that has a dense atmosphere. Titan is also the only object in our solar system except for earth that has liquids on the surface. Titan has just like earth a landscape with rivers and lakes it has a variating climate with wind and rain. The river and lakes are liquid methane and the atmosphere consists of nitrogen. The average surface temperature in -179 C or -290 F. Not even the most resistant living organisms that are known on Earth would ever survive on Titan and many scientists find it very unlikely that life could exist on Titan. However, it would not be theoretically impossible for life on Titan. Perhaps organisms that been developed on Titan differs from the one developed on Earth. Perhaps those lifeforms like freezing liquid methane just like we like water. Huygens probe that landed successfully on Titan in 2005 was not equipped to provide evidence for biosignatures. More probes to investigate Saturn’s moons has been proposed in the future, though.

credit  NASA/JPL-Caltech

In our solar system, the inner planets are terrestrial and the outer planets are gas giants and according to the theory of solar system formation, massive Jovians can only form in the cold outer regions of the system.

But still, it is very common that exosolar systems have so-called hot Jovians. A hot jovian is a gas giant that is orbiting close to its sun. The first one orbiting a sun-like star was discovered In 1995 by Michel Mayor and Didier Queloz around the star 51 Pegasi. One explanation could be that young large Jovians formed in the outer regions of their solar system gains enough gravitational force that it reduces the planet's orbital energy causing the planet to migrate inward. 827 hot Jovians and 139 warm Jovians have been discovered so far. If a jovian is in the habitable zone of its star it could have moons. Just like Titan the moon could have atmosphere and oceans and those oceans could be water instead of methane and the temperature could be similar to earth. Perhaps an alien civilization exists on a moon instead of a planet. The science fiction movie Avatar from 2009 takes place on the moon Pandora orbiting the gas giant Polyphemus in the Alpha Centauri A system. Alpha Centauri A does look like a pleasant home for exoplanets the star emits far less radiation than our sun, but no one is found so far.

We have not discovered any Exomoons yet because as those are very hard to detect and confirm using current techniques. In July 2017 Hubble Space Telescope found signs of a Neptune-sized exomoon around the planet Kepler-1625b. Theoretical it could be possible with James Webb Space Telescope in the future to detect images of exomoons. Some scientists estimate that there are as many habitable exomoons as habitable exoplanets. There are several candidates with possible habitable exomoons in the PHL exoplanet catalog. It is possible both in the Android app and in this website catalog to filter for candidates with possible habitable exomoons.