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Statistical Analysis of Near Earth Objects By Danielle Bisordi and Kristin Buckley Professor Florescu MA 331 December 3, 2009

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What is a Near Earth Object? Commonly referred to as NEO’s Commonly referred to as NEO’s Comets and asteroids that have been nudged by the gravitational attraction of nearby planets into orbits that allow them to enter the Earth's neighborhood 1 Comets and asteroids that have been nudged by the gravitational attraction of nearby planets into orbits that allow them to enter the Earth's neighborhood 1 Composed mainly of water and ice and are remnants of debris from the formation of the solar system ~4.6 billion years ago 1 Composed mainly of water and ice and are remnants of debris from the formation of the solar system ~4.6 billion years ago 1 We found data on the 11,726 NEO observations made by NASA in the last 10 years We found data on the 11,726 NEO observations made by NASA in the last 10 years

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Quantitative Data Types Year – year of near miss Year – year of near miss Month – month of near miss Month – month of near miss Miss Distance – Closest distance NEO gets to Earth Miss Distance – Closest distance NEO gets to Earth Velocity – relative velocity of NEO to earth Velocity – relative velocity of NEO to earth H – The diameter of an asteroid can be estimated from its absolute magnitude (H). The lower the H value, the larger the size of the object. 2 H – The diameter of an asteroid can be estimated from its absolute magnitude (H). The lower the H value, the larger the size of the object. 2

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Categorical Data: Class Types 3 Near Earth Asteroid (NEA) Types Atira (IEO – “Inner Earth Orbit”) - NEAs whose orbits are contained entirely with the orbit of the Earth Atira (IEO – “Inner Earth Orbit”) - NEAs whose orbits are contained entirely with the orbit of the Earth Atens (ATE) - Earth-crossing NEAs with semi- major axes smaller than Earth's Atens (ATE) - Earth-crossing NEAs with semi- major axes smaller than Earth's Apollos (APO) - Earth-crossing NEAs with semi-major axes larger than Earth's Apollos (APO) - Earth-crossing NEAs with semi-major axes larger than Earth's Amors (AMO) - Earth-approaching NEAs with orbits exterior to Earth's but interior to Mars' Amors (AMO) - Earth-approaching NEAs with orbits exterior to Earth's but interior to Mars'

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Questions Do the year or month have an effect on the quantity of near misses? Do the year or month have an effect on the quantity of near misses? Does the absolute magnitude and the relative velocity of the NEO have an effect on the miss distance? Does the absolute magnitude and the relative velocity of the NEO have an effect on the miss distance? Which class of NEOs have the closest near miss average and does the class type effect the velocity of the NEO? Which class of NEOs have the closest near miss average and does the class type effect the velocity of the NEO? Assuming there are more NEOs in existence than our sample data describes, is it likely that there are any NEOs that will have a miss distance of less than.0026 AU? Assuming there are more NEOs in existence than our sample data describes, is it likely that there are any NEOs that will have a miss distance of less than.0026 AU?

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Does the year have an effect on the quantity of near missed? First we made a histogram to determine the frequency of NEO appearance each year First we made a histogram to determine the frequency of NEO appearance each year From the year histogram we found that the year 2008 had the most NEO appearances. We also observed that the NEO appearances have been linearly increasing every year. From the year histogram we found that the year 2008 had the most NEO appearances. We also observed that the NEO appearances have been linearly increasing every year.

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Is the increase in NEO appearances every year a linear increase and if so what is the predicted number of NEOs to appear in 2012? Using the frequency of occurrence of each year we found the linear regression line of frequency vs. year and used that to approximate the predicted number of NEOs to appear in 2012 Using the frequency of occurrence of each year we found the linear regression line of frequency vs. year and used that to approximate the predicted number of NEOs to appear in 2012 This year (2009) there were 1422 NEOs. In 2012 we found there will be approximately This year (2009) there were 1422 NEOs. In 2012 we found there will be approximately 2016.

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Does the month have an effect on the quantity of near missed? We made a histogram to determine the frequency of NEO appearances each year We made a histogram to determine the frequency of NEO appearances each year From the histogram it was apparent that the most NEOs appear in January every year. From the histogram it was apparent that the most NEOs appear in January every year. There is also a second peak, much lower, in October There is also a second peak, much lower, in October

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Does the absolute magnitude and the relative velocity of the NEO have an effect on the miss distance? We plotted the absolute magnitude vs. miss distance and relative velocity vs. miss distance to determine whether there is any linear correlation between miss distance and absolute magnitude or miss distance and relative velocity We plotted the absolute magnitude vs. miss distance and relative velocity vs. miss distance to determine whether there is any linear correlation between miss distance and absolute magnitude or miss distance and relative velocity We also performed a multivariate linear regression to determine if these factors are statistically significantly effecting the miss distance We also performed a multivariate linear regression to determine if these factors are statistically significantly effecting the miss distance

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Does the absolute magnitude and the relative velocity of the NEO have an effect on the miss distance? (Continued…) From the plots we can see that both the magnitude vs. miss distance and the relative velocity vs. miss distance are linearly related From the plots we can see that both the magnitude vs. miss distance and the relative velocity vs. miss distance are linearly related It appears that the larger NEOs pass by Earth at a farther distance than the smaller NEOs It appears that the larger NEOs pass by Earth at a farther distance than the smaller NEOs Overall the velocity seems to increase with the miss distance, although it can also be inferred from the graph that the closer the NEOs get to the sun the faster they travel (as opposed to farther from Earth) Overall the velocity seems to increase with the miss distance, although it can also be inferred from the graph that the closer the NEOs get to the sun the faster they travel (as opposed to farther from Earth) From the linear regression test we found that both the relative velocity and the absolute magnitude are statistically significant in determining the miss distance From the linear regression test we found that both the relative velocity and the absolute magnitude are statistically significant in determining the miss distance

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Does the class of NEOs have an effect on the miss distance? First we make a box plot to visually inspect the data to determine whether it appeared that the miss distance differed between classes First we make a box plot to visually inspect the data to determine whether it appeared that the miss distance differed between classes Visually it appeared that the miss distance was effected by the class of NEO Visually it appeared that the miss distance was effected by the class of NEO We then performed an ANOVA test which confirmed our observation We then performed an ANOVA test which confirmed our observation The Apollo NEOs have the closest miss distance. The Apollo NEOs have the closest miss distance.

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Does the class type effect the velocity of the NEO? We analyzed the velocity vs. class data using the same techniques as in the previous slide We analyzed the velocity vs. class data using the same techniques as in the previous slide We found that the class types do have statistically significant different velocities. We found that the class types do have statistically significant different velocities. The Atira (Inner Earth Orbit) NEOs have the highest average velocity. The Atira (Inner Earth Orbit) NEOs have the highest average velocity.

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Assuming there are more NEOs in existence than our sample data describes, is it likely that there are any NEOs that will have a miss distance of less than.0026 AU? First we perform a t-test of the miss distances to see if the actual mean miss distance is greater than.0026 AU First we perform a t-test of the miss distances to see if the actual mean miss distance is greater than.0026 AU Then we find a 99% confidence interval for the mean to see if.0026 falls in that range Then we find a 99% confidence interval for the mean to see if.0026 falls in that range From the t-test we found that our null hypothesis can be rejected and that the actual mean miss distance is statistically significantly greater than.0026 AU From the t-test we found that our null hypothesis can be rejected and that the actual mean miss distance is statistically significantly greater than.0026 AU We can say with 99% confidence that no NEO will pass closer to earth than.2308 AU (Assuming the NEOs continue to behave in a similar manner as they have in the past ten years) We can say with 99% confidence that no NEO will pass closer to earth than.2308 AU (Assuming the NEOs continue to behave in a similar manner as they have in the past ten years)

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Conclusions The amount of NEOs in existence is linearly increasing The amount of NEOs in existence is linearly increasing More NEOs pass by Earth in January than in any other month More NEOs pass by Earth in January than in any other month The larger NEOs will miss colliding with Earth by a larger distance than the smaller ones. The larger NEOs will miss colliding with Earth by a larger distance than the smaller ones. The velocity of the NEOs gets slightly greater the farther away from Earth it becomes The velocity of the NEOs gets slightly greater the farther away from Earth it becomes The varying types of NEOs do have different average velocities and average miss distances. The varying types of NEOs do have different average velocities and average miss distances. It is highly unlikely that an NEO will pass closer to Earth than the Moon in the near future It is highly unlikely that an NEO will pass closer to Earth than the Moon in the near future Thus we’re probably not going to die in 2012 Thus we’re probably not going to die in 2012

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