Instructions You are piloting a spaceship through outer space and see an asteroid with a smooth enough surface to allow a landing. You decide to do some calculations before landing the spaceship on this asteroid. What would be the best angle of descent for the spaceship to ensure it suffers minimal or no damage? Please assume that the velocity of the spaceship when orbiting the asteroid is 1000 m/s and the gravitational acceleration at a height less than 100 km from the surface of the asteroid is 0.5 m/s? (and assume it is O at the height of more than 100 km) What is the minimal size of the asteroid which would allow the landing to occur if the ship's thrusters can provide the deceleration of -2 m/s2? Can you calculate the best approach trajectory (analytically or numerically using Mathematica)? Please use Mathematica or similar graphing software (i.e., MATLAB) to plot out the best approach trajectory. What simplifying assumptions did you have to make? What are the main difficulties you encountered? Would you agree to pilot the spaceship through the landing or would it be too risky in your opinion? What would you change about the problem's parameters to make the landing less risky? What would you do about the approach trajectory if you had to land on a really small asteroid? Post your answers to this discussion. After you post your answers, work with your classmates who have already posted to determine a correct answer to the following question: Would you agree to pilot the spaceship through the landing or would it be too risky in your opinion? Make sure to provide significant details in your replies based on your calculations. Additional Resources For this assignment, you will need to calculate the best approach using graphing software. Here are three potential options: e Desmos: This is a free online tool. e Free MATLAB Trial: "MATLAB Online: may be used with a trial license, though this must be verified through MathWorks upon choosing this option. The benefit of this option is that no software is installed on your system. You access the software through a web browser. e Free Mathematica Trial: The trial is only for 15 days