# Exoplanets

Exploring the universe

## Will we ever be able to travel to the stars

Will humans ever be able to travel to the stars and colonize habitable exoplanets?
Closest habitable exoplanet Proxima Centauri b is 4.25 light-years away. The fastest spacecraft is NASA robotic spacecraft Parker Solar Probe that was launched in 2018 it has a max speed of 192 000 meters per second that is 0,0006 percent of light speed. With that speed, it will take 7000 years to reach Proxima Centauri b. We need to get to a speed at least 10 percent of light speed to reach Proxima Centauri in a reasonable time. A reasonable time is 50 years if we consider the wait dilemma. In 50 years we will be able to build space ships that can reach the target destination much faster, so it will be more beneficial to wait.
We will never reach the stars using rocket engines because we would need more fuel than it is mass in the observable universe to reach 10 percent of light speed.
The rocket equation is

$$\Delta v =v_{e}\ln \frac{m+f}{n}$$
Where m is the mass of the vehicle, ve is the exhaust velocity of the rocket and f  is the mass of the fuel. If we solve f  from the rocket equation, we get:
$$f =me^{\frac{\Delta v }{v_{e}}}-m$$
If  we assume that the mass is equal to 1000 kg and exhaust velocity of 210,000 m/s which is the speed of our very best reaction engines, we get:
$$1000e^{\frac{3000}{21}}-1000 \approx 1*10^{65}$$
Compare that with the total amount of mass in the observable universe that is  $$1.5*10^{53}$$kg.

It would be theoretically possible to make the trip using nuclear fusion by detonating many nuclear bombs behind the spacecraft. Physicist Freeman Dyson and Ted Taylor at General Atomic worked with this idea in a project called Orion in 1958, but the Partial Test Ban Treaty of 1963 that forbid nuclear bombs in space ended the project. Another idea is to use a fusion rocket. Project Daedalus was a study conducted between 1973 and 1978 to design an unmanned interstellar spacecraft to reach Barnard's Star 5.9 light-years away. The trip was estimated to take 50 years, but the technology behind fusion rockets are complicated and we are not there yet.

A more efficient method is to use antimatter rockets when a subatomic particle collides with its respective antiparticle a large fraction of the rest mass is converted into energy. Depending on how much antimatter we could make it would be possible to reach a speed of 80 percent of light speed. The travelers on a ship with that speed only need to wait 3.2 years to arrive at Proxima Centauri b.
Because of time dilation from Einstein's special relativity :
$$t =\frac{t_{o}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$$

$$\Rightarrow \frac{4.25}{0.8}*\sqrt{1-0.8^{2}}=3.2.$$
Antimatter is produced in many experiments at CERN, but far from the amount that is needed it takes a lot of energy and it is hard to contain.

Credit Gerhard Janson pixabay

Another option is to travel faster than light. The Mexican theoretical physicist Miguel Alcubierre created an idea in 1994 which a spacecraft could travel at warp speed by using Albert Einstein's field equations in general relativity.
A signal in space cannot move faster than light, but the space itself can expand faster than light. The idea is that space is moving the ship just like a surfers board is moved by the water waves. This is mathematically possible, but one needs negative gravity. Negative gravity is produced by negative mass, not anti-matter which has positive gravity. Scientists have never observed negative gravity or mass, but there is nothing in the Einstein field equations that forbid it. Negative mass is equal to negative energy.  Dark energy is postulated to act in opposition to gravity and will perhaps work as negative energy. Dark energy explains why the universe is expanding at an accelerating rate and 72 percent of total energy in the universe consists of dark energy. If scientists figure out how to get this dark energy, perhaps warp drive like in Star-trek will be possible in the future.

The most promising option to travel to Proxima b is to use a solar sail read about the project here Breakthrough Starshot

Proxima Cen b Alcubierre drive

## Atmosphere on exoplanets

The chemical composition of an exoplanet atmosphere can tell us much about conditions on the planet and if it is potentially life bearing. Many planets it's discovered using the transit method. When a planet passes in front of its star a small drop of light will occur. By looking at the transit with different wavelength of the light scientists can find out the chemical composition of the atmosphere. Let's say if the planet does not have an atmosphere all colors (wavelengths) of the light will be blocked equally at the transit. But if the planet does have an atmosphere some atoms will absorb light better at certain wavelengths making the light not equally blocked. If the depth of the blocked light from the star is larger when being looked at a certain color with a spectrograph then the atmosphere will contain the element that is absorbing that color. This method is called transmission spectroscopy and to be able to find molecules like water scientist need to look at the longer wavelength in the infrared spectrum. Most of the discoveries of atmospheres are of hot Jupiters or hot Neptunes as the heated atoms or molecules will absorb light better at high temperatures.

The first detection of an atmosphere around an exoplanet was in 2001 when sodium was detected on the hot Jovian named HD 209458 b that is also known under the nickname Osiris.
Osiris that is located in the constellation Pegasus 159 light-years from us is known for several first discoveries in exoplanet research.
It was the first transiting exoplanet and the first planet to have its orbital speed and mass measured. The planet has an evaporating hydrogen atmosphere and containing oxygen and carbon. In 2013 water vapor was detected in the atmosphere of Osiris and several other hot Jovians like  XO-1b, WASP-12b, WASP-17b, and WASP-19b. Water vapor was also reported on  HAT-P-11 b in September 2014. HAT-P-11b is a Neptune sized exoplanet and that was also the first time any molecules was discovered on such a small planet.

In February 2016, it was announced that Hubble Space Telescope had detected hydrogen and helium in the atmosphere of 55 Cancri e. 55 Cancri e is a super-Earth exoplanet with a diameter just twice as Earth. 55 Cancri e is a very hot planet with an average temperature of 2,300 °C on the dayside. No water vapor was discovered on the planet. In 2018 iron and titanium was found in the atmosphere of a super-hot Jovian Kelt-9 b

The most recent discovery of an atmosphere was on GJ 3470 b. It is a Super-Earth about 14 earth masses. But it’s atmosphere contains hydrogen and helium and seems to lack heavier elements like methane and ammonia.

HD 209458 b XO-1 b WASP-12 b WASP-17 b WASP-19 b HAT-P-11 b GJ 3470 b KELT-9 b 55 Cnc e

## Teegarden two new Earth like exoplanets has been discovered

Teegarden star that is a very faint M-type red dwarf star was discovered in 2003 and was named after Bonnard Teegarden that was working at NASA's Goddard Space Flight Center

The star is 12.5 light years away and has a mass of 0.08 solar masses and luminosity of 0.00073 of our sun. The parallax was initially measured wrong and gave it a distance of only 7.5 light years away that would be the third nearest star after Alpha Centauri and Bernard star. Teegarden is now ranked the 24th nearest star system. Observations by the ROPS survey in 2010 showed variation in the radial velocity of the star suggesting it has a planetary system.
CARMENES that stands for "Calar Alto high-Resolution search for M dwarfs with Exoearths with Near-infrared and optical Échelle Spectrographs” at the Calar Alto Observatory announced evidence of two Earth-mass exoplanets orbiting the star within its habitable zone.

The news was announced a couple of days ago on June 18, 2019. The two planets have high earth similarity index and are located within its star habitable zone. Teegarden b is located in the optimistic habitable zone and Teegarden c is in the conservative zone. No transits of the planets have yet been seen by our astronomers. But because of the cosmic geometry, any alien astronomers living on Teegarden planets could use the transit method to discover Earth as we orbiting just in the right angle from their point of view. Teegarden b has the highest chance of having temperate surface environment.  However, as the planets are orbiting a red dwarf star their orbits are tidally locked and stellar activity from the star could be dangerous for life.

Here is a simulation of the solar system in our app here: Teegarden

Teegarden b Teegarden c

## European space agency upcoming exoplanet hunters

A new computer algorithm called Transit least squares has been tested on the old Kepler data. It resulted in the discovery of 18 Earth-sized exoplanets. Most of them are not good candidates for life as they are orbiting too close to their stars. But one of the new planets is in the habitable zone of its star. The planet is called EPIC 201238110.02 and is located on a distance at 522 light years from Earth.
Astronomers should now be able to find at least another 100 Earth-sized planets in the data from the Kepler mission with this method. Next generation land-based telescopes and space telescopes will also benefit from these algorithms in their search for Earth-like planets. This also bodes well for the upcoming missions planned by ESA.

When a planet transiting it star a small drop in brightness over time occur

Credit: NASA Ames

European space agency ESA is developing three space telescopes that will be used to study exoplanets. CHEOPS (CHaracterising ExOPlanets Satellite) and PLAnetary Transits and Oscillations of stars (PLATO) and Atmospheric Remote-sensing Infrared Exoplanet Large-survey (ARIEL).

Cheops
Cheops will be measuring the size of known transiting exoplanets, and that data will be compared with ELT observations to find rocky planets like earth. It will lift off at Europe's spaceport in Kourou, located in in the northeast of South America in French Guiana, between 15 October to 14 November 2019. The mission will have a duration of 3.5 years It will be placed at low-Earth orbit at an altitude of 700 km. In a competition children between the age of 8 and 14 from several countries submitted drawings related to exoplanets. Of 8000 drawings 2700 drawings were selected to be engraved on two titanium plaques that will be placed on the telescope, see all the drawings here: childrens drawings

Plato
Plato will be a follow-up mission to the very successful Kepler it will search for planetary transits around one million stars. Plato will be focusing on Earth-like planets in the habitable zone around other G-type stars. It will carry 34 telescopes operating in the visible spectrum. Its observations will determine the age, orbit, and composition with the goal to establish if an Earth-like exoplanet has an atmosphere. A knowledge that could be used for more detailed categorization like scanning for biomarkers. The project is scheduled for launch in 2026 and has a 4 years mission duration. Just like James Webb and Kepler, it will be orbiting the sun in the so-called Lagrange point.

Ariel
Plato will be followed by Ariel, scheduled for launch in 2028. Ariel will study the atmospheres in great details of a sample 1000 exoplanets. Ariel will just like Plato orbiting the sun in the so-called Lagrange point.

EPIC 201238110.02 Plato Cheops Ariel

## How do we calculate the distance to the stars

Already antique astronomers used their curiosity and innovative engineering abilities to determine the large distances in our Solar system. When humans start sailing on the oceans they saw how the airframe disappeared before the mast when a boat was passing the horizon which leads to the speculation that Earth was round. This notation was established by 3rd century BC by Greek astronomy. In 240 B.C the Greek astronomer Eratosthenes that also is known as the father of geography as he introduced the concept of longitude and latitude and draw a map over at that time the known world. He made a very accurate measurement of the circumference of the Earth. In the city of Syene 800 kilometers south of Alexandria (Egypt) there where a famous well. Precisely at summer solstice once a year the Sun's rays shone straight down into the well. At the same time in Alexandria. Eratosthenes measured the length of the shadow from a stick and calculated the angle to:

$$\tan^{-1} \frac{d_{shadow}}{d_{stick}}\approx 7.2^{\circ }$$
7 degree is 1/50th the circumference of a circle and knowing the distance to Syene is 800 kilometers the earth circumference should be 50 times that distance 40 000 kilometers.

Or using trigonometry:
$$2\pi \frac{800000}{\tan 7.2^{\circ }}\approx 40241005$$

Another Greek astronomer Aristarchus of Samos at the same time calculated the distance to the Moon (R). By looking at a lunar eclipse and calculating how long time it took for the Earth shadow to cross over the Moon that takes 3 hours and 40 minutes (t) it will take 29 days for the Moon to orbit an entire revolution around the Earth (T). He estimated the distance to 60 earth radii (r) that is correct.

$$\frac{\pi R}{r}=\frac{T}{t}$$

$$\Rightarrow R\approx 60r$$

He also estimated the distance to the Sun. During a solar eclipse, the Moon covers almost the entire disc. This tells us that the Sun is larger than the Moon and farther away. During half moon he assumed that the Moon forms a right angle with the Sun and Earth he measured that angle to 87 degrees.

$$\frac{R_{\odot}}{60r}=\cos 87^{-1}\approx 20$$
He came to the conclusion that the Sun is 20 times farther away from the Moon. This is wrong the Sun is 400 times farther away from the Moon as the angle is closer to 90.
On a side note: trigonometric functions had not yet been invented the ancient greek used geometrical relations to find proportions.

The first measurement of the distance to a planet was made by Gian Domenico Cassini. In 1672, He used a technique called parallax to measure the distance to Mars. If you hold up your thumb at one arm distance look at with just the left eye and then the other you will see that object farther away is shifting position that is caused by the separations of your eyes. You are watching the object from two different positions. The distance the thumb seems moving is its parallax. If you know the distance between your eyes and the angle by which your thumb moved against the background, you can calculate the length of your arm. By making an observation on two different places at Earth one can calculate the distance to objects far away in the same way.
To measure the distance to a star like Proxima Centauri that is 4.24 light-years away. One could take pictures of the star from two points when Earth is at one side of the Sun and then six months later when Earth is on opposite sides of the Sun and then calculating the parallax angle that more distant stars seem moving. The parallax angle Proxima shifting is 0.77 arc second one arc second is 1/3600 of a degree. A distance to a star was calculated for the first time in 1838 by Friedrich Bessel who measured the parallax of 61 Cygni as 0.314 arc second 11.4 light-years away. To measure large distances to stars the unit parsec (pc) is often used instead of light-years. A parsec is a distance that the parallax angle is 1 arc second that is 3.26 light-years. Parallax can only be used to find distances under 100 parsecs away

To measure the luminosity that is the total amount of energy emitted per time by an astronomical object or the brightness a logarithmic scale are used that is called the absolute magnitude. The sun has a magnitude of -27 and the dimmest objects visible with the naked eye has a magnitude of 6. The apparent magnitude is the magnitude of the object seen at 10 parsecs away. The brightness of a star is inversely proportional to the square of its distance.
$$L\sim \frac{1}{D^{2}}$$

French astronomer Charles Messier cataloged 110 astronomical objects the closest large galaxy was cataloged M31 in 1764. He thought it was a nebula within our galaxy. The object is also known as Andromeda and is visible with the naked eye. When astronomers discovered a variable star called novae in Andromeda in 1917 they noticed that it was 10 times less bright than similar stars in our galaxy. A Cepheid variable star is a very bright star that pulsates in a predictable way.
once the period has been measured its luminosity can be estimated. Then the distance to the object could be calculated in parsec with this formula

$$d=10^{(m-M+5)/5}$$

where m is the apparent magnitude and M the absolute magnitude of the Cepheid. Edwin Hubble in 1925 calculated that the galaxy 1.5 million light-years away. Modern calculations show it is 2.5 million light-years away or 778 000 parsec.

Image credit: NASA/JPL-Caltech

Andromeda galaxy is blueshifted it moving towards the milky way due to gravitational forces but all distant galaxies are redshifted they are moving away because the universe is expanding. The velocity of a galaxy is proportional to its distance from us by the equation
$$v=Hd$$
Where H is the Hubble constant that is estimated to be 70.0 km/sec/Mpc
Objects like quasars that are the ultraluminous nuclei of galaxies are extremely redshifted. For example, the quasar 3C 273 has a redshift of 0.158 which means it moving away at a speed of 44000 km/s (0.158 * speed of light)
using Hubble's law its distance could be calculated to 2 billion light-years or 620 Mpc.
The most distant object GN-z11 has a redshift on 11.09 and is 13.39 billion light-years away (actually it is much further away as space has been expanding during the time it takes the light to reach us).

Andromeda Hubble