Dr. SaMeH S. Ahmed

Associate Prof. of Environmental Engineering

Elliptic orbit2


Elliptic orbit


In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity less than 1; this includes the special case of a circular orbit, with eccentricity equal to zero. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit). In a wider sense it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1.

In a gravitational two-body problem with negative energy both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit.

Examples of elliptic orbits include: Hohmann transfer orbitMolniya orbit and tundra orbit.


Velocity

Under standard assumptions the orbital speed (v,) of a body traveling along elliptic orbit can be computed from the Vis-viva equationas:

v=sqrt{muleft({2over{r}}-{1over{a}}
ight)}

where:

The velocity equation for a hyperbolic trajectory has either + {1over{a}}, or it is the same with the convention that in that case a is negative.

[edit]Orbital period

Under standard assumptions the orbital period (P,!) of a body traveling along an elliptic orbit can be computed as:

P=2pisqrt{a^3over{mu}}

where:

Conclusions:

[edit]Energy

Under standard assumptions, specific orbital energy (epsilon,) of elliptic orbit is negative and the orbital energy conservation equation (the Vis-viva equation) for this orbit can take the form:

{v^2over{2}}-{muover{r}}=-{muover{2a}}=epsilon<0

where:

Conclusions:

  • For a given semi-major axis the specific orbital energy is independent of the eccentricity.

Using the virial theorem we find:

  • the time-average of the specific potential energy is equal to 2ε
    • the time-average of r−1 is a−1
  • the time-average of the specific kinetic energy is equal to –ε

[edit]Flight path angle

The flight path angle is the angle between the orbiting body's velocity vector (= the vector tangent to the instantaneous orbit) and the local horizontal. Under standard assumptions the flight path angle phi satisfies the equation:

h, = r, v, cos phi

where:

[edit]Equation of motion

See orbit equation

[edit]Orbital parameters

The state of an orbiting body at any given time is defined by the orbiting body's position and velocity with respect to the central body, which can be represented by the three-dimensional Cartesian coordinates (position of the orbiting body represented by x, y, and z) and the similar Cartesian components of the orbiting body's velocity. This set of six variables, together with time, are called the orbital state vectors. Given the masses of the two bodies they determine the full orbit. The two most general cases with these 6 degrees of freedom are the elliptic and the hyperbolic orbit. Special cases with less degrees of freedom are the circular and parabolic orbit.

Because at least six variables are absolutely required to completely represent an elliptic orbit with this set of parameters, then six variables are required to represent an orbit with any set of parameters. Another set of six parameters that are commonly used are the orbital elements.

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Office hours


Sunday:     12-1

Monday:     12-1

Tuesday:     10-12

Wednesday: 10-11

You are welcome to contact me by at any time

You  may also contact me via WhatsApp group, ..

Ext. 2524

Civil Eng. Students

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Love your department and be proud of your field of study

As we approaching the second midterm exams..  Get ready and remember our offices are open to answer you . do not hesitate to .contact me if you have difficulties


For CE 370 students : I do apologize for did not attend the extra lab session that proposed to be on Wednesday at 6 am.  Sorry

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Announcements


My Dear Students

Please visit the  announcement box for the relevant course and make sure that you can download and upload easily, otherwise

.contact me  to sort it out

There will be an orientation session in the midell of this term to help you select your track in Civil and Environmental Engineering

Event

Special Issue

Electrical Power Resources: Coal versus Renewable Energy



  Published Online on January 2016


Mining Engineering


Mining engineering is an engineering discipline that involves practice, theory, science, technology, and the application of extracting and processing minerals from a naturally occurring environment. Mining engineering also includes processing minerals for additional value.

Environmental Engineering

Environmental engineers are the technical professionals who identify and design solutions for    environmental problems. Environmental engineers provide safe drinking water, treat and properly dispose of wastes, maintain air quality, control water pollution, and remediate sites contaminated due to spills or improper disposal of hazardous substances. They monitor the quality of the air, water, and land. And, they develop new and improved means to protect the environment.

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Tawasl

تواصل

College of Eng. MU

http://mu.edu.sa/ar


Univeristies

Universities I've worked in


Assuit University (Home University), Egypt


Imperial College, London, UK


Faculty of Engineering, Al-Mergeb University, Libya


King Saud University, KSA

,Majmaah University


Majmaah University has a very nice web page that provide  all information regarding deanships, colleges, activities,  campuses and many others. Search your request in
http://mu.edu.sa/en

Also visit

My Academic Pages

https://www.researchgate.net/profile/Sameh_Ahemd

and give me


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How many red balls we need to make balance 

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Egypt vs Tunisia (Handball final)  30/1/2016


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Course 2016/17-1


  1. Computer Applications in Surveying  CE 473
  2. Surveying 1 CE 370
  3. Photogrammetry CE 474
  4. Surveying II  CE 371
  5. Design I  (round 4) CE 498




The Rules of Life

Rule #7

Latest

Member of the Editorial Board: " Journal of Water Resources and Ocean Sciences"  2013

https://www.researchgate.net/profile/Sameh_Ahmed5/?ev=hdr_xprf

Participating in The Third International Conference on Water, Energy and Environment,(ICWEE) 2015 - American University of Sharjah, UAE 24-26 March 2015 with a Paper and Poster

New article

Recovery of Titania from Waste-Sludge of Majmaah Water Treatment Plant

"Production of Titania Nano-particles from Wast-

Sludge

Coming soon



Results of M2 CE311

Student Conference



Participation  in the 6Th Student Conference

With a paper and oral presentation

From the Senior Design Project CE499 -35

See inside, the paper, and presentation

CE 370 Course

Surveying  I -  CE 370 - 2016-2017-1




Power point


Sheets


Lecture notes


Second Midterm Exam



Results


Model Answer
Inside, please follow:

Student Performance Records

CE 371 Course

Surveying II - CE 371 - 2016-2017-1




Lectures





First midterm exam


Lab


Results

See Inside

Student Performance Records

CE473 Course

Computer Applications in Surveying

CE 473



Lecturers


Power point


Sheets


Exams + Quizzes


Results




CE 474 Course

2015-2016-2 - Photogrammetry  CE474




Available 0-1-2-3-4 Power point

Available

Quizzes 2 and 3 with model Answer

Quizzes
Available Chapter 1,2,3,4,5 Lecture notes

Report 1  Cameras Report

Y

60 marks Exams

See Inside

Student Performance Records


CE 360 Course

Environmental Engineering 1



CE 360: Environmental Engineering 1

37-2

Y PP0-1-2-3,4 Power point
Y 1,2,3,4,5 Chapters

Water quality Poster + Climate Change Reports
will be announced (Quiz #2 will be using D2L- Online Quizzes

Y

Quizzez 2,3 and 4 with model answer and results Exams and results

GE 306 Course

Engineering Report Writing


GE 306: Engineering Report Writing

CE 499 Course

Senior Design 2 - CE 499

Meeting on 14-4-2015

Second Best paper from Senior Design Projects in 2015

Paper title:

Evaluation of Groundwater Quality Parameters using Multivariate Statistics- a case Study of Majmaah, KSA

Students:

Abdullah A. Alzeer

Husam K. Almubark

Maijd M. Almotairi

CE 360-Summer Course

Environmental Engineering I


Welcome to CE360 second Term 2015-2016 

Engineering Practice

 Engineering Practice GE 307

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Contact me

Mobile: 00966598311652

[email protected]

Civil and Environmental Engineering Department
College of Engineering, Majmaah University
Majmaah, P.O. 66, 11952, KSA

Thank you

Your frequent visit to my website has helped  a lot to get the 2nd place in the university competition in the  year 1434-2013... Thanks very mush and please keep following my work

زيارتكم المتكررة لموقعي ساهمت في حصولي على المركز الثاني لاحسن المواقع الشخصية بجامعة المجمعة ...لكم جميعا خالص شكري وتقديري

CE 212 - Summer Course

Properties and Strength of Materials 1

CE 212

Y from PP0 to PP 6 + PDF Power points
Y Midterm #2 + Model Answer + results Exams
Y lab 3 Labs

Solution of Quiz 4 + Results HW


CE 311- Summer Course

Soil Mechanics and Foundation Engineering

CE 311

M2+ model Answer + PP 1-9 = PDF 1-9 all are available

Sheets 2 + 4 with model Answers

Results of M2



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