Tag Archives: Curiosity

Spring 2019/Lecture 5/Perturbed Motion – 6 Feb 2019

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Sorry for the missed lectures on Friday and Monday. I was out sick. Assignments are due on Friday. We covered perturbations to orbital motion. We examined contributions from gravitational and nongravitational sources to the two-body motion.

Sign up for updates here: https://mailchi.mp/d95b0d174531/odcourse

Slides: L5 Slides – Perturbed Motion

[youtube https://www.youtube.com/watch?v=HZjksLbF4go&w=560&h=315]

Previous lectures:

 

 

Spring 2019/Lecture 4/Two Body Problem – 30 Jan 2019

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We resumed today with orbital mechanics. We covered the two-body problem, introduced Kepler’s problem (time doesn’t relate well to true anomaly), and sprinted to the state transition matrix. We will resume with perturbations and additional bodies considered on Friday.

Sign up for updates here: https://mailchi.mp/d95b0d174531/odcourse

Slides: L4 Slides – Two Body Problem

[youtube https://www.youtube.com/watch?v=Mx6PEYk_RQE&w=560&h=315]

Previous lectures:

 

 

Statistical Orbit Determination

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Class time/Preliminary Notes

I will be teaching a statistical orbit determination course this summer. This will be on my own time. All lectures will be posted to YouTube. I will be teaching the course out of Bob Schutz’s, Byron Tapley’s, and George H. Born’s, Statistical Orbit Determination. Feel free to use any textbook you desire but the problems and solutions will be assigned from this text. I have included some precursor notes in question and answer format on statistics and probability below.

AppendixA-ProbabilityAndStatistics

Syllabus

AEM_StatisticalOrbitDetermination_Syllabus_CRS

STATISTICAL ORBIT DETERMINATION

EXECUTIVE SUMMARY:

Orbit Determination (OD) is the problem of determining the best estimate of the state of a spacecraft whose initial state is unknown, from observations influenced by random and systematic errors, using a mathematical model that is not exact. Mordern OD is used to support all space missions from JSpOC’s observations of artificial Earth satellites to the International Space Station’s trajectory planning incorporating elements of probability, statistics, and matrix theory. A special projects class is needed to cover this vital part of the space curriculum that arguably makes the backbone of any space program.

DISCUSSION:

Modern OD approaches have been developed by the NASA Jet Propulsion Laboratory (JPL) to fulfill Earth and planetary navigation requirements and at the NASA Goddard Space Flight Center (GSFC) and the Department of Defense Naval Surface Weapons Center in applications of satellite tracking to problems in geodesy, geodynamics, and oceanography. The Joint Space Operations Center (JSpOC) at Vandenberg Air Force Base, the Conjunction Assessment Risk Analysis (CARA) at GSFC, and Trajectory Operation Officers (TOPO) at Johnson Space Center (JSC) use modern OD techniques in applications of satellite tracking, conjunction assessment, and protecting vital assets from the International Space Station to the National Reconnaissance Office (NRO) spy satellites.

Clearly, OD is an important part of any space mission. The proposed class will use the classical text, Statistical Orbit Determination, by Drs. Byron Tapley, Bob Schutz, and George Born. This basic OD course will cover:

  • Introduction to OD problem
    • Dynamic system and associated state
    • Observations are non-linear functions of state variables
    • Classical well-determined approach
    • Modern over-determined approach
  • Observations to measure satellite motion
    • Ground-based systems: laser, radiometric, etc.
    • Space-based systems: GPS, etc.
    • Error sources and media corrections
  • Non-linear OD reduced to linear state estimation
    • Application of linear system theory
    • Incorporation of algorithms to computational environment
    • Sequential processing of observations
    • Control of real-time processes

This will be supported by background and supplemental information in:

  • Probability and Statistics
  • Review of Matrix Concepts
  • Examples of State Noise and Dynamic Model Compensation
  • Solution of the Linearized Equations of Motion

Students can expect to incorporate their classroom knowledge into real-life by building optical and radiometric sensors supporting The University of Alabama’s new satellite ground station.

LECTURES:

Lecture 1 – Orbit Determination Concepts

Lecture 2 – Orbital Mechanics Review

Post-Flight Analysis Report (PFAR) of RX1

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SUMMARY:

Christopher R. Simpson built a rocket to pass his Level 1 (L1) certification from the National Association of Rocketry (NAR). The rocket was a kit from Madcow Rocketry; the “Frenzy,” [1]. The RX1 used an Aerotech H550ST-14A, “Super Thunder,” motor with a total impulse of 71.9 lb-sec and a burn time of 0.57 sec. Construction of the rocket, flight, and recovery are reviewed to analyze and critique operations.

Post-Flight Analysis Report (PFAR) attached here: PFAR-RX1 (26 Feb 2018)

YouTube link to flight: https://www.youtube.com/watch?v=Xqff5scf-00

ACKNOWLEDGEMENTS:

A big thank you to Karson Holmes for certifying/critiquing me and William Ledbetter for making the trip to watch the fun take off! Also, a special thanks to Alabama Rocketry for allowing me to use their adapter.

RESOURCES:

Rocket Used: https://www.madcowrocketry.com/4-frenzy/

Motor/Supplier Used: https://csrocketry.com/rocket-motors/aerotech-rocketry/motors/38mm/dms-rocket-motors/aerotech-h550-14a-super-thunder-dms-rocket-motor.html

Alabama Rocketry Facebook Page: https://www.facebook.com/alabamarocketry/

Pheonix Missile Works Facebook Page: https://www.facebook.com/groups/58541022592/

 

 

 

2017 ESPRMC Graduate Research Symposium – The University of Alabama

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I will be presenting “Benefits of Tracking Aids on a 1U CubeSat,” on Thursday, April 13 at the 2017 ESPRMC Graduate Research Symposium. Dr. O’Neill was my co-author. I hope to see you there.

Abstract:

Incoporating active/passive tracking aids into the design of a university/high school CubeSat mission promotes good space stewardship. Tracking aids are necessary for improved tracking covariance of CubeSats. Tracking aid support and design-space cost are covered. Reflectarrays, patch array(s), and deployable antennas show the potential benefit of transmitting data over S-band frequencies and tracking aids that enhance the mission capabilities. Passive and active tracking aids with low impact on the mission provide reduced covariance of CubeSats orbit tracks shown through use of modeling tools.

Cesium Demo Using STK Scenario/TLE Data

Coming Soon: Orbital Mechanics/Astrodynamic Problem Solutions

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While in the midst of preparing for a journal paper I decided that I wanted to showcase my abilities. I will solve all the problems from Vladimir Chobotov’s Orbital Mechanics, Third Edition, and Richard Battin’s An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition and post the solutions online. I hope to have this done by January 2.

Not only will this be a good review for myself but it will showcase my abilities to solve problems relating to the field I want to enter. Hopefully, it will prove to be a valuable tool in the future.

As for the featured picture: I am in the process of getting myself certified Level 1 with STK. I dropped this scenario into Cesium while I was practicing and exploring STK before the exam. My exam is due December 22. I will let you know the results soon!

Lessons from Gene Kranz's "Failure Is Not An Option"

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FAILURE IS NOT AN OPTION is an overview of Gene Kranz’s time as a controller with the newly formed Mecury Program to the last Apollo mission. He describes the growth of a burgeoning new space program, the success and the failures, and the men and women that took America to the moon.

The dedication of Gene’s team and his resolve to be TOUGH and COMPETENT following the Apollo 1 disaster that claimed the lives of Ed White, Roger Chaffee, and Gus Grissom are exemplary of a leader. His resolve to forge his team from mere engineers to operators is incredible. His resolve paid off when he and his team helped bring home Apollo 13 alive and safe. Time and time again Gene makes critical decisions based on his extensive preparation, the implicit trust he has for his fellow controllers, and his gut. A new group of young controllers seems to join the old with each mission. With each mission the young become old with their experience in the trenches.

Several lessons that can be gained:

  • Preparation: “Failing to prepare is preparing to fail.”-John Wooden. Gene’s team was more than a group of engineers. They were operators. They knew the system and their spacecraft extensively inside and out.
  • Trust: If you don’t trust your team to make the right decisions then why do they work for you? There was an implicit bond of trust between Gene, his underlings, and his peers.
  • Mentorship: One day you will be replaced. If the system is to run smoothly  you have to encourage individual growth while showing them the ropes.

What does this mean for me?

In Dr. O’Neill’s laboratory we often face critical, time-constrained decisions. My ability to answer them is a reflection of my capabilities. In my current down-time I am focused on improving my CAD, Orbit Analysis, and Coding knowledge.

 

 

 

Lessons from Gene Kranz’s “Failure Is Not An Option”

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FAILURE IS NOT AN OPTION is an overview of Gene Kranz’s time as a controller with the newly formed Mecury Program to the last Apollo mission. He describes the growth of a burgeoning new space program, the success and the failures, and the men and women that took America to the moon.

The dedication of Gene’s team and his resolve to be TOUGH and COMPETENT following the Apollo 1 disaster that claimed the lives of Ed White, Roger Chaffee, and Gus Grissom are exemplary of a leader. His resolve to forge his team from mere engineers to operators is incredible. His resolve paid off when he and his team helped bring home Apollo 13 alive and safe. Time and time again Gene makes critical decisions based on his extensive preparation, the implicit trust he has for his fellow controllers, and his gut. A new group of young controllers seems to join the old with each mission. With each mission the young become old with their experience in the trenches.

Several lessons that can be gained:

  • Preparation: “Failing to prepare is preparing to fail.”-John Wooden. Gene’s team was more than a group of engineers. They were operators. They knew the system and their spacecraft extensively inside and out.
  • Trust: If you don’t trust your team to make the right decisions then why do they work for you? There was an implicit bond of trust between Gene, his underlings, and his peers.
  • Mentorship: One day you will be replaced. If the system is to run smoothly  you have to encourage individual growth while showing them the ropes.

What does this mean for me?

In Dr. O’Neill’s laboratory we often face critical, time-constrained decisions. My ability to answer them is a reflection of my capabilities. In my current down-time I am focused on improving my CAD, Orbit Analysis, and Coding knowledge.

 

 

 

Maxwellian Distribution

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This is a brief dip into velocity distribution. It is not intended to be cited nor be academically through. Rather it will hopefully provide some insight and give you links to use other than Wikipedia.

Velocity Space

Imagine a container of particles. Gas particles. As these particles are whizzing about we notice this cloud of molecules seems to be equally spread out in all directions.

Maxwell-Boltzmann Distribution Drawings_0

This is for several reasons:

  • Brownian motion (random movement)
  • Molecules prefer to be at equilibrium for the whole system
    • They don’t want to be moving in the same direction

If we were to examine the velocities of the particles using velocity space, a 3D system

Maxwell-Boltzmann Distribution Drawings_0(1)

Velocity Space System

describing a particle’s velocity, we would find that they are evenly distributed as well.

 

 

 

 

 

We can imagine this as a shell. The velocities of all the particles will be distributed in a common range in order to achieve equilibrium.

Maxwell-Boltzmann Distribution Drawings_1(1)

2D View of Velocity Distribution Shell

 

Velocity Distribution Function

This is where the Maxwellian distribution will come into play. In a real system we know that a molecule will not maintain constant velocity over time. There’s van der Waal’s forces, ionic, covalent, and metallic interactions, collisions, and a whole host of other things that can interact with the molecule. Since the main focus is rarified gas or a dilute gas we can assume intermolecular forces are negligible, (equilibrium kinetic theory).

The velocity distribution function for gas molecules in thermal equilibrium is based on symmetry. One molecule loses 5 m/s, another gains 5 m/s.

Maxwell-Boltzmann Distribution Drawings_2

Maxwellian Distribution of Velocity

Average Quantity, Q

With N, the total number of molecules, and f(Ci), the velocity distribution we can find the average quantity. We find N from integrating the number of molecules with Ci velocity.

This average quantity can be use for anything that uses velocity: start thinking about momentum.

Some things to remember from our assumptions with equilibrium kinetic theory:

  • Intermolecular forces negligible
  • Collisions occur in a unit area
  • All momentum is transferred through the collision process

So we could find normal stress, σ, pressure, P, or etc…

Maxwellian Distribution

Neglecting the derivation we are led to the Maxwellian distribution so that we don’t have to plot every single molecule. The Maxwellian distribution will give the probability that a molecule has speed a certain range of speed.

The information gained from using a Maxwellian distribution:

  1. The most probable speed of the molecules present
  2. The average speed of the molecules present
  3. The root mean square speed, Vrms
  4. Equation of state for perfect gas

Acknowledgements

Thanks to Dr. Wang for teaching Physical Gas Dynamics, where my notes from that class have served as the outline for this article.

I have provided links throughout this article specifically avoiding Wikipedia to help give you more references. Please credit your sources if you use them in your writing. (MLA) (AIAA)