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Elliptical Orbits

The Time Travelers Web Site!

This is not just science fiction. By Richard Doran

 

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Gravity Friction Launch Elliptical Orbit Circular Orbit Planet Assist

How does a craft reach distant planets? Discover the intent behind rockets and trajectories. I hope this will be general enough to be understood and detailed enough to be educational.

The information contained in this page is for estimating purposes only.

When you think you have the right stuff, enter this challenge. When you are finished designing the craft, Press Launch and see what happens.

First Challenge: [Thrust and the Design of Elliptical and Circular Orbits]

 

 

 

 

Challenge: [Space Craft to Mars]

 

Rocket Flight Velocity

  1. Compute the rocket mass ratio: mr = mi / mf
  2. mr = Rocket Mass Ratio (No units) – In multi stage rockets the mass ratio’s are equal.

    mi = Rocket Mass Initial, mf = Rocket Mass Final. (matching units required)

  3. Compute the burnout velocity: vb = si g ln mr (for the initial boost)
  4. vb = Velocity at Burnout (ft/sec) or (m/sec), si = Fuel Specific Impulse (Sec) Liquid is about 250 sec., Solid is about 200 sec, g = 32.2 (ft / sec2) or 9.8 (m / sec2) Gravitational acceleration, ln = Log to the base e (2.71828), mr = Rocket Mass Ratio (No units).

    System

    Specific Impulse, si

    Ratio Thrust to Engine Wt.

    Liquid Propellant

    200-300

    50 to 80

    High-Energy Liquid Propellant

    340-440

    50 to 80

    Nuclear Energy

    400 to 900

    50 to 80

    Free Radicals

    400 to 1,800

    50 to 80

    Solar Heat Transfer

    400 to 500

    0.05

    Ion

    5,000 to 20,000

    0.0005

  5. Compute the half range angle: Cos q max = ((gc re)2 – (gc re2 vb2))0.5 / (gc re - rbo vb2 / 2)
  6. g = 32.2 (ft / sec2) or 9.8 (m / sec2) Gravitational acceleration, re = The radius of the Earth (3963 miles or 6377.8 km), rbo = Rocket Burnout Radius, vb = Velocity at Burnout (ft/sec) or (m/sec).

  7. Compute the final velocity of the rocket: vf = ve ln mr (relative, in orbit, velocity)

vf = Final Velocity (ft / sec.) ve = Discharge velocity of the propellant (ft / sec.) They really have books for this stuff! If you go on-line and use a search engine, you will find more specific information for this. Use 10,000 ft / sec unless you get a specific number from a book, ln = Log to the base e (2.71828), mr = Rocket Mass Ratio (No units)

Satellite Flight Velocity, Period and Escape Velocity

  1. Compute the satellite velocity in a given orbit: vs = ((gc re) / re + h)0.5
  2. g = 32.2 (ft / sec2) or 9.8 (m / sec2) Gravitational acceleration, re = The radius of the Earth (3963 miles or 6377.8 km), h = elevation above sea level in feet.

  3. Compute the time required for one revolution: radius of the earth is approximately 3963 miles, Add to that the total elevation above the Earth surface (h) to get the total radius (r) of rotation. Twice the radius is the diameter (d). Then the circumference is [(pi) d], or [2 (pi) r]. The circumference divided by the velocity is the period per time. For geostationary orbit the period is one revolution every 24 hours.
  4. [2 (pi) (3963 + h miles)] / (vs miles /hour) = 24 hours

  5. Compute the satellite escape velocity: vx = vs (2)0.5

vx = Velocity of escape (Ft / sec), vs = (Calculated above)

Interplanetary Flight launch velocity and flight time

  1. Compute the Major Axis of the flight path: ma = (d1 + dt) / 2
  2. d1 = Distance of launch body from the Sun, dt = Distance of the target body from the Sun, ma = Length of the major axis

  3. Compute the specific mechanical energy of the system: E = -(gs rs2) / 2 ma
  4. rs = 2.285 X 109 feet (697 x 106 meters), gs = Gravity of the Sun 900 ft / sec2 (274.3 m / sec2), E = specific mechanical energy, ma = Length of the major axis

  5. Compute the satellite orbit Perigee velocity: vp = (2 E + 2 (gs rs) / rp)0.5
  6. rs = 2.285 X 109 feet (697 x 106 meters), gs = Gravity of the Sun 900 ft / sec2 (274.3 m / sec2), rp = Radius at the perigee

  7. Compute the Required velocity increment for an orbiting satellite to reach escape velocity: Velocity increment = velocity at the perigee of planetary transit – Earth orbit velocity; vi = vp - vo
  8. vp = Velocity at the perigee (Ft / sec), vo = Earth orbit velocity

  9. Compute the Period of the flight: t = 2 (pi) ma1.5/ (gs rs)0.5 = The time to travel from the first planet to another planet. (Same variables used above)

Pub. McGraw Hill, Author Tyler G. Hicks; Page 8.12 - 8-18; ISBN 0-07-028735-X

Pub. Professional Publications, Inc., Author Michael Lindeburg, P.E. Page 16-9 ISBN 0-912045-72-8

Caution: Worm Holes ahead

Home References History Rockets Craft Planets Orbits Aliens Future Support Time

Gravity Friction Launch Elliptical Orbit Circular Orbit Planet Assist