Space Debris Sample

Local coordinates

Here, we will study space debris. We will set up equations of motion that are local to a particular spacecraft. We will then investigate what happens if a small part of the spacecraft is detached and has a small velocity relative to the spacecraft. You will need new files for three-dimensional motion, but they can be modified from existing ones. The key thing is to make sure that the equations that you are solving are the ones in the WE13 box below. Each of you will choose a different altitude for your spacecraft and get a slightly different value for the angular velocity of the spacecraft in its circular orbit.

Workshop Exercise WE13:

A. The Kessler effect

Write brief notes (about half a page) on the Kessler effect. In your discussion, make reference to the number and size distribution of objects in low-Earth orbits and the timescales on which the debris problem becomes critical. Use your own words and give references for your discussion. Try and access the scholarly literature e.g., using the online Library Search in Canvas or Google Scholar.

 

B. Drifting around your spacecraft

It can be very dangerous stepping outside of your spacecraft. If you push a tool slightly away from you, you will push it into a new orbit that can see it drift away from the spacecraft. Even more worryingly, you could find yourself drifting away and unless you have a tether or some personal boosters, you may never get back to the craft. In this exercise, you will explore the motion of objects around a spacecraft that have speeds very slightly different from the spacecraft itself. The coordinate system we use is a Cartesian one which is dragged around with the spacecraft so that the y-axis always points away from the Earth and the x-axis along the spacecraft’s orbit (in the direction of travel) which we will assume is circular.

 

Space Debris

We will restrict ourselves to motion in the orbital plane so we will set z to zero and Vz similarly can be set to zero. As a result, any object outside the spacecraft can be given initial (x,y) coordinates and (Vx,Vy) velocity components and then we can work out the path it follows.

The equations describing the motion are

Space Debris

The constant ? is the angular velocity of the spacecraft on its circular orbit.

Answer:

 

Workshop Exercise WE13: 

  1. The Kessler effect

The Kessler syndrome, proposed by NASA scientist Donald J. Kessler in 1978, is a scenario in which the density of objects in low Earth orbit is high sufficiently due to space pollution that collisions between objects could cause a chain reaction, with each collision generating space debris, increasing the likelihood of further collisions. The problem of space debris has been exacerbated by the tests of multiple satellite-killing missiles, which have left massive leftover debris fields. The Kessler Effect has taken hold, and researchers are looking at the consequences for tiny satellites like CubeSats. The current technology in a multipronged strategy, including the capacity to detect space debris in orbit, execute obstacle avoidance, have adequate shielding to withstand tiny hits, and other approaches to reduce the problem.

The harshness and unpredictability of the space environment can have unintended consequences, such as collisions, for satellites in orbit. When these objects collide, the debris that is created has the potential to cascade, causing other debris to collide with it in orbit. It is prudent to examine existing mitigation measures now that we have a better knowledge of the gravity of the orbital debris situation. Methods for orbital debris mitigation have been identified by NASA and ESA, as well as other international organisations. Given the growing body of knowledge about the impacts of orbital debris, it is evident that considerable worldwide efforts are required to secure the long-term usage of the orbits that circle our planet. Kessler wrote in 2009 that modelling results showed the debris environment was already unstable, "such that any attempt to achieve a growth-free small debris environment by eliminating sources of past debris will likely fail because fragments from future collisions will be generated faster than atmospheric drag will remove them." The distribution of trash in orbit, for example, might make space operations and satellite utilisation in certain orbital regions challenging for many generations.

References



B. Drifting around your spacecraft

we have create the model for the motion of the spacecraft using the given sets of differential equation for which we plot and simulate the trajectory of the spacecraft, we have initialize different initial velocity and position of spacecraft and simulate the model on the same figure as shown in the below results, we have investigate the trajectory for the velocity of 7000, 7800 and 8500m/s and the initial position of 2000, 2500 and 3000km, the algorithm computes the angular velocity of the spacecraft according to the altitude and initial velocity of spacecraft, from the simulation results we can observed that all the investigated trajectory are periodic in nature as its is exactly returning to the same point of start, the simulation result with the MATLAB code is describing below.

 

% Clear data and figures clc clear close all % Initialize global variables global R V % Radius of earth rearth=6371e3; % Spacecraft 1: For the velocity of 7e3m/s and 2000km at altitude % Initial position of spacecraft pos0=[0 7e3 2000e3+2*rearth 0 0 0]; % Orbit radius R=pos0(3); % Orbit velocity V=pos0(2);

Space Debris