Escape Velocity Problem
Primary Faculty Mentor’s Name
Dr. Thinh Kieu
Proposal Track
Student
Session Format
Paper Presentation
Abstract
University of North Georgia
Department of Science and Mathematics
Students
Instructor
Name: Richard Fields
Email: RAFIEL5455@ung.edu
Name: Vinh Bui
Email: VPBUI3450@ung.edu
Name: Thinh Kieu
Email: Thinh.kieu@ung.edu
Escape Velocity of a Rocket
Many problems arise in Aerospace and Aeronautical Engineering in which there is a need for a satellite, spacecraft, or astronaut to be launched into Earth’s orbit. In order to execute this, one must know the initial velocity the rocket must possess for it to escape Earth’s gravitational pull. The first step is to translate descriptions of real world phenomena and data into mathematical models. In this case, we find a sufficient condition for initial velocity, so that when the rocket is fired from the earth, it never returns. In order to model the problem, we use Newton’s second law of gravitation. The equation obtained from the above approach is a nonlinear second order differential equation for the position of the rocket. Then we use the theory of differential equations to obtain an implicit, exact solution for velocity. After this, we implement the model on MATLAB. A program is written to solve for the position vs time and the velocity vs time of the rocket from launch to the arrival into orbit. Next, we use the interpreted solution to answer the question raised in the project. Finally we check the model prediction with known facts.
The process used in this research can be used to further understand more complex variations to the escape velocity problem. It can also be used as a tool to understand and mathematically model other natural phenomena.
Keywords
Escape velocity model, exact solution, approximate solution, nonlinear differential equation, numerical method
Location
Room 1909
Presentation Year
2015
Start Date
11-7-2015 9:00 AM
End Date
11-7-2015 10:00 AM
Publication Type and Release Option
Presentation (Open Access)
Recommended Citation
Fields, Richard A. and Bui, Vinh Phuc, "Escape Velocity Problem" (2015). Georgia Undergraduate Research Conference (2014-2015). 13.
https://digitalcommons.georgiasouthern.edu/gurc/2015/2015/13
Escape Velocity Problem
Room 1909
University of North Georgia
Department of Science and Mathematics
Students
Instructor
Name: Richard Fields
Email: RAFIEL5455@ung.edu
Name: Vinh Bui
Email: VPBUI3450@ung.edu
Name: Thinh Kieu
Email: Thinh.kieu@ung.edu
Escape Velocity of a Rocket
Many problems arise in Aerospace and Aeronautical Engineering in which there is a need for a satellite, spacecraft, or astronaut to be launched into Earth’s orbit. In order to execute this, one must know the initial velocity the rocket must possess for it to escape Earth’s gravitational pull. The first step is to translate descriptions of real world phenomena and data into mathematical models. In this case, we find a sufficient condition for initial velocity, so that when the rocket is fired from the earth, it never returns. In order to model the problem, we use Newton’s second law of gravitation. The equation obtained from the above approach is a nonlinear second order differential equation for the position of the rocket. Then we use the theory of differential equations to obtain an implicit, exact solution for velocity. After this, we implement the model on MATLAB. A program is written to solve for the position vs time and the velocity vs time of the rocket from launch to the arrival into orbit. Next, we use the interpreted solution to answer the question raised in the project. Finally we check the model prediction with known facts.
The process used in this research can be used to further understand more complex variations to the escape velocity problem. It can also be used as a tool to understand and mathematically model other natural phenomena.
