# Essay Example on Relationship between an exoplanets radius and Position

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Aim My aim is to investigate the relationship between an exoplanets radius and position to its host stars brightness What is an Exoplanet For a planet to class as an exoplanet it must follow certain criteria the criteria dictates that the mass of the planet must be equal to or less than 30 Jupiter masses the planet must orbit around a star it cannot be free floating extensive validation and follow up observations must be done to ensure that it is a true exoplanet To summarise an exoplanet is a planet which orbits a star other than our own sun In 2013 reports said that there could be up to 40 billion earth like sized exoplanets which lie within their own habitable goldilocks zones How can we detect Exoplanets There are several methods of detecting an exoplanet the most used and reliable are Radial Velocity Methods Transit Methods Radial Velocity Method This is where you look for changes in a star whether it is motion redshift blueshift or no shift When motion is detected in a star this is known as a wobble This occurs when the exoplanet orbits the star and the gravitational pull of the moving planet creates a wobble

The gravitational pull of the planet can also cause redshift and blueshift when the planet is being pulled towards or away from the earth Redshift when a planet is moving away from the earth its wavelengths are stretched creating longer wavelengths which appear on the red end of the spectrum Blueshift when a planet is moving towards the earth its wavelengths are compressed creating shorter wavelengths which appear on the blue end of the spectrum Transit Method This is when a change in the star's brightness is observed due to a planet orbiting in front of it Difference between the brightness and luminosity of a star The apparent brightness of a star is how bright it is observed from earth Luminosity is the amount of light it emits from its surface To calculate the brightness of a star you must first know the distance between the star and the observer This can be known from its parallax Then use the formula below to work it out Source 1 Website The website I have used is relevant to my assignment and aim and a reliable source of information It is reliable as it was created and written by a researcher from the Instituto de Astrofisica de Canarias To investigate the relationship between an exoplanets position and its stars brightness i have chosen to further investigate the transit method This method is established around the small drop in apparent brightness of a star which occurs when a planet transits in front of it blocking out the light and therefore decreasing the brightness of the star Note that the planet does not affect the luminosity of the star The transit method in action looks like this If you were to record the apparent brightness of a star it would not lie flat only when the planet is not passing in front of the star would it be flat

When the planet passes it would create a dip in the graph showing the decrease in brightness This is shown below in an example I have recorded an example of the transit method please refer to Graph 1 in the appendix Source 2 Experiment Method To simulate a star I used a cardboard box with a hole 7 cm in radius cut into the side I covered the hole with greaseproof paper to even out the light Inside the box I left a light bulb to emit the light from my star I cut out planets from cardboard paper with varying radii First I recorded the base apparent brightness then stood the planets 16 cm away from the sun and recorded the apparent brightness of each planet on an app on my phone I took the apparent brightness of each planet 5 times to be able to calculate an accurate average Using my results I have calculated the drop in apparent brightness by using a formula which uses the radii of the planet and star I also calculated what fraction the apparent brightness had dropped Planet 1 Radius 1 5 cm Drop in apparent brightness 1 5 2 7 2 0 045 Fraction of drop 1153 790 1153 0 31 Planet 2 Radius 2 cm Drop in apparent brightness 2 2 7 2 0 08 Fraction of drop 1153 917 1153 0 204 Planet 3 Radius 2 5 cm Drop in apparent brightness 2 5 2 7 2 0 127 Fraction of drop 1153 247 1153 0 786 Planet 4 Radius 3 cm Drop in apparent brightness 3 2 7 2 0 18 Fraction of drop 1153 167 11653 986 Planet 5 Radius 3 5 cm Drop in apparent brightness 3 5 2 7 2 0 25 Fraction of drop 1153 109 1153 0 91 Planet 6 Radius 4 cm Drop in apparent brightness 4 2 7 2 0 33 Fraction of drop 1153 41 1153 0 96 Based on the results I calculated I created a graph marking the drop of apparent brightness relating to the size of the radius of the planet From this graph you can see that there is a correlation between the drop in apparent brightness and the exoplanets radii As the radius increases as does the drop in apparent brightness this is sufficient evidence to prove a relationship between an exoplanets radius and its host stars brightness

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