OneStopGate.Com
OnestopGate   OnestopGate
   Thursday, March 28, 2024 Login  
OnestopGate
Home | Overview | Syllabus | Tutorials | FAQs | Downloads | Recommended Websites | Advertise | Payments | Contact Us | Forum
OneStopGate

GATE Resources
Gate Articles
Gate Books
Gate Colleges 
Gate Downloads 
Gate Faqs
Gate Jobs
Gate News 
Gate Sample Papers
Training Institutes

GATE Overview
Overview
GATE Eligibility
Structure Of GATE
GATE Coaching Centers
Colleges Providing M.Tech/M.E.
GATE Score
GATE Results
PG with Scholarships
Article On GATE
Admission Process For M.Tech/ MCP-PhD
GATE Topper 2012-13
GATE Forum




GATE 2025 Exclusive
Organizing Institute
Important Dates
How to Apply
Discipline Codes
GATE 2025 Exam Structure

GATE 2025 Syllabus
Aerospace Engg..
Agricultural Engg..
Architecture and Planning
Chemical Engg..
Chemistry
Civil Engg..
Computer Science / IT
Electronics & Communication Engg..
Electrical Engg..
Engineering Sciences
Geology and Geophysics
Instrumentation Engineering
Life Sciences
Mathematics
Mechanical Engg..
Metallurgical Engg..
Mining Engg..
Physics
Production & Industrial Engg..
Pharmaceutical Sciences
Textile Engineering and Fibre Science

GATE Study Material
Aerospace Engg..
Agricultural Engg..
Chemical Engg..
Chemistry
Civil Engg..
Computer Science / IT
Electronics & Communication Engg..
Electrical Engg..
Engineering Sciences
Instrumentation Engg..
Life Sciences
Mathematics
Mechanical Engg..
Physics
Pharmaceutical Sciences
Textile Engineering  and Fibre Science

GATE Preparation
GATE Pattern
GATE Tips N Tricks
Compare Evaluation
Sample Papers 
Gate Downloads 
Experts View

CEED 2013
CEED Exams
Eligibility
Application Forms
Important Dates
Contact Address
Examination Centres
CEED Sample Papers

Discuss GATE
GATE Forum
Exam Cities
Contact Details
Bank Details

Miscellaneous
Advertisment
Contact Us


Laws of astrodynamics

Looking for GATE Preparation Material? Join & Get here now!

** Gate 2013 Question Papers.. ** CEED 2013 Results.. ** Gate 2013 Question Papers With Solutions.. ** GATE 2013 CUT-OFFs.. ** GATE 2013 Results.. **

Laws of astrodynamics

Laws of astrodynamics

The fundamental laws of astrodynamics are Newton's law of universal gravitation and Newton's laws of motion, while the fundamental mathematical tool is his differential calculus.

Standard assumptions in astrodynamics include non-interference from outside bodies, negligible mass for one of the bodies, and negligible other forces (such as from the solar wind, atmospheric drag, etc.). More accurate calculations can be made without these simplifying assumptions, but they are more complicated. The increased accuracy often does not make enough of a difference in the calculation to be worthwhile.

Kepler's laws of planetary motion may be derived from Newton's laws, when it is assumed that the orbiting body is subject only to the gravitational force of the central attractor. When an engine thrust or propulsive force is present, Newton's laws still apply, but Kepler's laws are invalidated. When the thrust stops, the resulting orbit will be different but will once again be described by Kepler's laws.

Escape velocity

The formula for escape velocity is easily derived as follows. The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy. The specific potential energy associated with a planet of mass M is given by

- G M / r \,

while the specific kinetic energy of an object is given by

v^2/2 \,

Since energy is conserved, the total specific orbital energy

v^2/2 - G M / r \,

does not depend on the distance, r, from the center of the central body to the space vehicle in question. Therefore, the object can reach infinite r only if this quantity is nonnegative, which implies

v\geq\sqrt{2 G M / r}

The escape velocity from the Earth's surface is about 11 km/s, but that is insufficient to send the body an infinite distance because of the gravitational pull of the Sun. To escape the solar system from the vicinity of the Earth requires around 42 km/s velocity, but there will be "part credit" for the Earth's orbital velocity for spacecraft launched from Earth, if their further acceleration (due to the propulsion system) carries them in the same direction as Earth travels in its orbit.

Formulae for free orbits

Orbits are conic sections, so, naturally, the formula for the distance of a body for a given angle corresponds to the formula for that curve in polar coordinates, which is:

r = {a \over (1 + e \cos \theta) }.

The parameters are given by the orbital elements.

Circular orbits

Although most orbits are elliptical in nature, a special case is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M is

\ v = \sqrt{\frac{GM} {r}\ }

where G is the gravitational constant, equal to

6.672 598 � 10−11 m3/(kg�s2)

To properly use this formula, the units must be consistent; for example, M must be in kilograms, and r must be in meters. The answer will be in meters per second.

The quantity GM is often termed the standard gravitational parameter, which has a different value for every planet or moon in the solar system.

Once the circular orbital velocity is known, the escape velocity is easily found by multiplying by the square root of 2:

\ v = \sqrt 2\sqrt{\frac {GM} {r}\ } = \sqrt{\frac {2GM} {r}\ }.



Discussion Center

Discuss/
Query

Papers/
Syllabus

Feedback/
Suggestion

Yahoo
Groups

Sirfdosti
Groups

Contact
Us

MEMBERS LOGIN
  
Email ID:
Password:

  Forgot Password?
 New User? Register!

INTERVIEW EBOOK
Get 9,000+ Interview Questions & Answers in an eBook. Interview Question & Answer Guide
  • 9,000+ Interview Questions
  • All Questions Answered
  • 5 FREE Bonuses
  • Free Upgrades
GATE RESOURCES
 
  • Gate Books
  • Training Institutes
  • Gate FAQs
  • GATE BOOKS
     
  • Mechanical Engineeering Books
  • Robotics Automations Engineering Books
  • Civil Engineering Books
  • Chemical Engineering Books
  • Environmental Engineering Books
  • Electrical Engineering Books
  • Electronics Engineering Books
  • Information Technology Books
  • Software Engineering Books
  • GATE Preparation Books
  • Exciting Offers



    GATE Exam, Gate 2009, Gate Papers, Gate Preparation & Related Pages


    GATE Overview | GATE Eligibility | Structure Of GATE | GATE Training Institutes | Colleges Providing M.Tech/M.E. | GATE Score | GATE Results | PG with Scholarships | Article On GATE | GATE Forum | GATE 2009 Exclusive | GATE 2009 Syllabus | GATE Organizing Institute | Important Dates for GATE Exam | How to Apply for GATE | Discipline / Branch Codes | GATE Syllabus for Aerospace Engineering | GATE Syllabus for Agricultural Engineering | GATE Syllabus for Architecture and Planning | GATE Syllabus for Chemical Engineering | GATE Syllabus for Chemistry | GATE Syllabus for Civil Engineering | GATE Syllabus for Computer Science / IT | GATE Syllabus for Electronics and Communication Engineering | GATE Syllabus for Engineering Sciences | GATE Syllabus for Geology and Geophysics | GATE Syllabus for Instrumentation Engineering | GATE Syllabus for Life Sciences | GATE Syllabus for Mathematics | GATE Syllabus for Mechanical Engineering | GATE Syllabus for Metallurgical Engineering | GATE Syllabus for Mining Engineering | GATE Syllabus for Physics | GATE Syllabus for Production and Industrial Engineering | GATE Syllabus for Pharmaceutical Sciences | GATE Syllabus for Textile Engineering and Fibre Science | GATE Preparation | GATE Pattern | GATE Tips & Tricks | GATE Compare Evaluation | GATE Sample Papers | GATE Downloads | Experts View on GATE | CEED 2009 | CEED 2009 Exam | Eligibility for CEED Exam | Application forms of CEED Exam | Important Dates of CEED Exam | Contact Address for CEED Exam | CEED Examination Centres | CEED Sample Papers | Discuss GATE | GATE Forum of OneStopGATE.com | GATE Exam Cities | Contact Details for GATE | Bank Details for GATE | GATE Miscellaneous Info | GATE FAQs | Advertisement on GATE | Contact Us on OneStopGATE |
    Copyright © 2024. One Stop Gate.com. All rights reserved Testimonials |Link To Us |Sitemap |Privacy Policy | Terms and Conditions|About Us
    Our Portals : Academic Tutorials | Best eBooksworld | Beyond Stats | City Details | Interview Questions | India Job Forum | Excellent Mobiles | Free Bangalore | Give Me The Code | Gog Logo | Free Classifieds | Jobs Assist | Interview Questions | One Stop FAQs | One Stop GATE | One Stop GRE | One Stop IAS | One Stop MBA | One Stop SAP | One Stop Testing | Web Hosting | Quick Site Kit | Sirf Dosti | Source Codes World | Tasty Food | Tech Archive | Software Testing Interview Questions | Free Online Exams | The Galz | Top Masala | Vyom | Vyom eBooks | Vyom International | Vyom Links | Vyoms | Vyom World
    C Interview Questions | C++ Interview Questions | Send Free SMS | Placement Papers | SMS Jokes | Cool Forwards | Romantic Shayari