Reference no: EM132257893

Project - Satellite Orbits and Gravity Assist

Project Description

In this project, you will not do any coding, but you will be required to use Matlab to run two ready- made Matlab code files:

• Gravity_Assist.m: This is the code of the Matlab program that will simulate the launching of a spacecraft and the gravity assist phenomenon. You will not need to understand how the program works and will not need to edit this file at all. However, if you find the code fun to play with, you are more than welcome to modify it but please use the original code provided to you to complete the project requirements. I will use the original code to test the results that you provide me so if the results do not run properly on the original Matlab code, you will lose marks.

• Gravity_Assist_Data.m: This is the data file that you will edit. You will need to put your ID number (for example, "Student_ID = 2013123450;") on top and then fill in data about the firing of the rocket engine of a spacecraft that is located on Earth's surface (i.e., traveling with Earth on its orbit around the Sun) to control its trajectory and path.

This is what you will have to do:

1. Download both files and save them on your computer in any directory you like. They must be placed together in the same directory.
2. Run Matlab (Version 2010 or later should be fine) and open the two files in the editor.
3. Edit the "Gravity_Assist_Data" files with proper values and save the file.
4. Run the "Gravity_Assist" file in Matlab and observe the results. The program will automatically load your data and use it in the simulation
5. If the results of the simulation are not satisfactory, go back to step 3.
6. Repeat the whole process for each of the required scenarios of the project.
7. When you are satisfied with all of your results, email me all of your data files at once.

Editing Data in the file Named "Gravity_Assist_Data.m"

This file contains all the data you input that will be used by the system to simulate launching and maneuvering the spacecraft to achieve specific missions (for example travel around the sun or meet other planets (i.e., Mars, Jupiter, and Saturn). To speed up the process of doing the simulation and yet have reasonably accurate results, the simulation is done in steps of 1 minute. The data has to be provided in the form of sets of three values that are defined as follows

[FiringMinute]: Rocket Engine Firing Instant measured in minutes from start of Simulation. The simulation evaluates the position of the spacecraft and planets in steps of 1 minute. This parameter specifies which minute the rocket engine will be fired from the start of the simulation. This parameter must be a positive integer.

[EnginePower]: This represents the power (as a percentage) that the engine will operate at during that minute of the simulation. That is, when the rocket engine is fired at a specific minute, this parameter will specify if the rocket engine is fired at full power (EnginePower = 100) for example, or at one third of its power (EnginePower = 33.33) or any other value. This parameter must be a positive real number between 0 and 100.

[DirectionAngle]: This is the direction of Engine Thrust (in degrees). This will specify the direction at which you want the spacecraft to go to by firing the rocket engine, with 0 Degree being the positive x-axis and positive angles increase going counter-clockwise. This parameter can be any real number, but limit it to (0 to 360 degrees or -180 to 180 degrees).

The data is input in the data file as lines of code that appear as follows:

Fire_Time_and_Duration(FiringMinute_1) = [EnginePower_1 DirectionAngle_1];

Fire_Time_and_Duration(FiringMinute_2) = [EnginePower_2 DirectionAngle_2];

Fire_Time_and_Duration(FiringMinute_3) = [EnginePower_3 DirectionAngle_3];
... ... ... ...
Fire_Time_and_Duration(FiringMinute_N) = [EnginePower_N DirectionAngle_N];

Important Note 1: To escape Earth's gravity, you will have to place at least 10 to 15 minutes at the beginning of the simulation (at Minute 1 or any later minute at which you wish to launch the rocket) of continuous rocket firing. If you don't, your rocket will be launched but may not have enough power to escape Earth's gravity so it will crash few minutes later. So, at the beginning, you will have to start with something that may look like as given in attached file.

This will launch the satellite at Minute 40, the rocket engine will continue firing until minute 49 (total of 10 minutes) in the direction of 17 Degrees at the beginning but few minutes later the direction will increase a little. In this case, the rocket may have enough speed to escape Earth's gravity completely. If it does not, add few more rocket firing after minute 49 and see the results.

Important Note 2: Consider the total firing duration in your data file to represent the total fuel that is used. That is, if you fire the engine of the rocket at full power for one minute, the fuel used is 1, if you fire the engine at 50% power for 6 minutes, the total fuel used is 3, and if you fire the engine at 75% power in one minute and 25% power in another minute, the fuel used is 1, and so on.

Helpful Note: Very often, you may need to change a value such as direction of firing engine for many entries in the data file. It is easier to put any specific value in a variable (such as "a", "b", "c", ... ) and use that variable in all lines in which you need that value as in the following:

This will save you a lot of time when editing the data file.

Project Requirements

You are required to complete 4 independent tasks:

1. GEO Orbit Around Earth: Launch the spacecraft into a circular GEO orbit around Earth. You will need to fire the engine of the spacecraft at the beginning to launch it, then you will have to adjust its orbit to take a shape of almost a circle. Time the orbit period by calculating the difference in minutes from the time the spacecraft is at a specific position with respect to Earth to the time of reaching the same position the next time. Ensure that this duration is as close to 1 day (1440 minutes) as possible (±3% is acceptable). The change in altitude of the satellite should also be relatively small to be able to assume that it is circular orbit (Perigee and apogee of orbit within ±3% of the orbit of a GEO is acceptable). Any amount of fuel can be used for this mission. Remember to time the orbit of the satellite after you have done all orbit adjustments (i.e., after the last minute of rocket firing).

2. Crashing on Earth After One Year: Launch the spacecraft into space and get it to crash on Earth after around one year (i.e., around 60*24*365.25 = 525,960 minutes) from launch time (±2% is acceptable). You can launch the satellite using any amount of fuel initially (i.e., in the first 200 minutes) and then never use any fuel after the initial launch. The crash on Earth should happen after 1 year from the last rocket firing.

3. Take Close-Up Pictures of Mars, Jupiter, and Saturn and then Leave Solar System: Put the spacecraft on a path that will make it pass by the three planets (Mars, Jupiter, and Saturn) and get benefit of gravity assist to increase its speed. Eventually let the spacecraft exit the region shown in the left graph of the program (i.e., the spacecraft will be out of view if it crosses 1x109 km from the sun in any of the 4 sides). You can use any amount of fuel at the beginning of the launch (first 100 minutes of simulation). However, after you pass by Mars, you only have 3 minutes of fuel using the full rocket engine power (100% of engine power). You can alternatively use less than 100% of rocket engine power to extend the duration longer than 3 minutes (for example, if you use 50% rocket engine power, you will be able to use rocket engines for 6 minutes, and so on). This remaining 3 minutes of fuel can be used to do fine adjustments of the path of your spacecraft as it travels from Mars to Jupiter and then to Saturn. You must pass within 150,000 km from the center of each of the three planets so that your spacecraft gets great pictures of them.

4. Take Close-Up Pictures of Complete Surface of Jupiter and Return to Earth in 500,000 Minutes: An atmospheric phenomenon has just happened on the surface of Jupiter and is expected to disappear soon. Your mission is to send the spacecraft to Jupiter very quickly, let it visit Jupiter, make nearly two rotations around Jupiter (slightly less than two rotations is acceptable) at any altitude and then return to crash on Earth. The round trip (Earth - Jupiter - Earth) must not take longer than 500,000 minutes. You can use a maximum of 100 minutes of fuel with 100% rocket engine power for the whole trip.

Hints for the Project Missions

Part 1
• Start launching the rocket at any time and any direction you wish, then change the direction of engine firing to put the rocket in a circular orbit. The simplest way of achieving this would be to fire the engine in a specific direction and observe the maximum distance that the space craft reaches before it comes back to Earth. Adjust that maximum distance to be the radius of a GEO satellite. Once this is achieved, you can time your rocket to do an engine firing at an angle of 90 degrees our of phase with respect to the original rocket firing that takes place at exactly the highest point of the orbit. Adjust the firing to achieve an orbit duration of exactly 1 day.

Part 2
• Since you are allowed to use fuel only at the beginning, you will have to launch the spacecraft and put it in an elliptical orbit (with low or large eccentricity) around the sun that has a period of exactly 1 year and hope that it will find Earth at the right place and right time when it returns back to the same position 1 year later. Another method would be to put the spacecraft in an orbit that keeps it close to Earth (an orbit that is almost similar to Earth's orbit) in a controlled way that will bring it back to Earth after 1 year. Remember that an elliptical orbit around Earth will probably not work because to have an orbit around Earth with a period that is around 1 year will mean that the orbit is so large, and therefore it will probably be affected by gravity of the Sun or other planets at specific points resulting in a distorted elliptical orbit that may not crash the spacecraft on Earth.

Part 3
• Launch the spacecraft from Earth towards Mars and let approach Mars from the back side. Don't use too much fuel (because it will just speed past Mars and miss Jupiter), and don't use too little fuel (because it will take too much time to reach Mars and probably not be able to go to Jupiter while it is in the right position.

• Determine on which side is the spacecraft approaching each of the planets. Based on this, determine when, for how long, and in which direction you need to fire the engine to adjust the path of the spacecraft. Remember that shorter early engine fires may do the same job as longer late engine fires.

• If you need to correct the path of the spacecraft, do it in small increments. Also, never do multiple adjustments at once, because you will not be able to figure out the effect of each adjustment on the path of the spacecraft. Always do individual adjustments in each step.

• If a change results in the wrong modification, the opposite change will probably do the job. For example, if the firing of the engine in the direction of 70 degrees produces wrong results, than firing the engine in the direction 180+70 degrees will probably do the job. Also, if firing the rocket engine earlier does not work, try firing the rocket engine at a later time, and so on.

• You can tell the effect clearly by observing the minimum distance that you get when approaching the different planets. These are indicated on the title, x-label, and y-label of the two graphs produced by the simulation program.

• The y-label of the left graph gives the simulation minute from the start of the simulation. Use this to determine which minute of the simulation you need to perform the next engine firing.

• It is better to optimize the path of the spacecraft from the start to a specific point. Once you are satisfied with that first segment of the path, you can proceed with optimizing the following segment of the path, and so on by adding new rocket engine firing after the optimized path. Remember that a rocket firing will change the path of the spacecraft after that firing not before it.

Part 4
• Fire the rocket engine for a relatively long time putting the spacecraft on a path to Jupiter. Make sure that the path of spacecraft makes a close encounter with Jupiter but not hit it. When it approaches Jupiter, slow it down significantly to put it in an orbit around Jupiter (don't stop it completely). After it makes around two revolutions (slightly less than 2 rotations is fine, but one rotation or less is not acceptable). One the two revolutions are completed, fire the rocket engine with all the fuel you have remaining to make the space craft go towards Earth and crash on its surface.

Attachment:- Introduction to Satellite Communications.rar