Circular, Elliptical and Parabolic/Hyperbolic Orbital Analysis Go
1) Plot Sub-orbital, orbital and escape trajectories around planets in the solar system knowing Burnout velocity (Vbo) and Flight-path angle at burnout (f).
2) Determine distance traveled from liftoff to impact (X) along planet curvature and sub-orbital flight path knowing Maximum altitude at burnout (Hb) and Down range distance at burnout (Xb).
3) Free flight angle from liftoff to impact (y), Sub-orbital flight time or orbital period (T), Planetary orbital velocity (Vcs), Planetary escape velocity (Ve) and Solar system escape velocity (Vsun) are all displayed in red for easy review.
4) Zoom-in to see near-planet trajectories for parabolic (e=1) and hyperbolic (e>1) flights when burnout velocity (Vbo) and flight path angle (f) are specified.
5) Determine velocity at origin planet sphere of influence (V00) and Flight time from burnout to destination orbit (T) for parabolic and hyperbolic trajectories (e>1).
6) View detailed instructions, StarTravelManual.pdf, by clicking D’Click for Instructions on the main screen.
Heliocentric and Hohmann Orbital Transfer Analysis Go
7) Determine minimum energy (i.e. velocity) required for heliocentric and Hohmann transfer orbits from Earth to other planets in the solar system and the Moon.
8) Determine velocity change from liftoff to burnout (dV) required for orbital insertion into heliocentric orbits and Hohmann Transfers to the planets and the Moon.
9) Predict spacecraft velocity of approach with destination planet while on the transfer ellipse.
10) Predict time of flight from burnout in Earth orbit to interception of destination planet.
11) Specify miss distance for the computation of heliocentric dV and time of flight.
12) Solar System Calculator displays current position of the planets, distance from Earth to the planets and orbital periods of the planets in the solar system.
Relativistic Star Travel Analysis Go
13) Determine Earth elapsed time and star ship elapsed time (proper time) for relativistic star travel (0.3c < V < 1.0c).
14) Determine starship Mass Ratio requirements as a function of relativistic speed and exhaust velocity.
15) Display Doppler color shift on forward and aft star light as viewed from the starship.
16) Use one of three acceleration-velocity profile options for travel to the stars:
a) Constant velocity (G = 0, V = constant).
b) Constant acceleration (G = constant, Vmax = speed of light (c) if distance is great enough). See note below.
c) Constant acceleration then constant velocity coast (G = constant, Vmax = constant).
Note: Constant velocity and constant acceleration, Options (a) and (b) are not practical for realistic star travel. For example, unbounded acceleration at modest G-loading will rapidly allow a starship to approach the speed of light (at 1G acceleration a starship will attain the speed of light within 1 year proper time). As a starship approaches the speed of light infinite energy and therefore infinite Mass Ratio (MR) is required. Instead, the method of accelerating to a modest coast velocity, Option (c) is the preferred method, making star travel feasible within the lifetime of a human being at moderate acceleration (0.1G’s to 1.0G’s) and modest maximum velocity (0.1c to 0.5c).
Rocket and Satellite Trajectory Analysis NEW! Go
17) Determine ballistic trajectory of rockets and missiles launched vertically, horizontally and everything in between.
18) Specify initial trajectory by inserting flight path angle at liftoff (q1), flight path angle at insertion (q2), time from liftoff to roll initiation (T1), and time from liftoff to insertion (T2).
19) Automatically displays the actual liftoff profile as either vertical launch or horizontal launch using specified orbital insertion data.
20) Determine altitude at burnout, range at burnout, velocity at burnout, Cd at burnout, maximum altitude, time from liftoff to apogee, time from liftoff to perigee, maximum range (suborbital) and time from liftoff to impact (suborbital) for single stage and two stage rockets. Plot and print numerous curves for flight profile visualization.
21) Atmospheric air density varies exponentially with altitude and drag coefficient (Cd) varies with rocket airspeed.
22) Import Cd verses Mach number curves previously generated using AeroDRAG & Flight Simulation and AeroWindTunnel version 220.127.116.11 or later.
VASIMR Constant Power Analysis NEW! Go
23) Perform a Variable Specific Impulse Magnetoplasma Rocket (VASIMR) analysis or a standard constant specific impulse rocket analysis by simply specifying starting Isp and ending Isp or constant Isp for heliocentric flight to planets and stars.
24) Determine time of flight, coast time, distance traveled during powered flight, distance traveled during coast, propellant mass required, mass fraction, velocity increment (dV) during powered flight, velocity at start and end of powered flight, specific impulse at start and end of powered flight, acceleration at start and end of powered flight, and finally thrust at start and end of powered flight.
25) Plot thrust verses time, mass flow rate verses time, velocity verses time, distance traveled verses time, specific impulse verses time, mass flow rate verses exhaust velocity, thrust verses exhaust velocity, rocket acceleration (Gs) verses time, rocket mass verses time, trajectory from Earth to destination planet and finally a detailed VASIMR drawing with component descriptions.
Sub-orbital, Orbital and Escape Trajectory Analyses Back
As illustrated in Figure-1 trajectories around a massive object like the Earth, Mars and the Moon follow one of a family of curves called conic sections. Depending on the specific energy (E), angular momentum (h) and mass (G*M) of a body the eccentricity (e) of an orbit will determine if the transfer orbit is a circle (e=0), ellipse (e<1), parabola (e=1) or hyperbola (e>1). The orbital elements of a body including the eccentricity (e) of an orbit are determined by burnout velocity (Vbo), flight path angle at burnout (f), burnout altitude (Hb) and down range distance (Xb) of an object for a two-body astrodynamic analysis. Because there is not enough space here to fully detail the orbital mechanics used in StarTravel please refer to the reference list in the included instructions (StarTravelManual.pdf).
Figure-1, Conic sections defined by eccentricity (e) and the other orbital elements.
To perform sub-orbital, orbital and escape trajectory analyses click Suborbital, orbital and escape trajectory under Trajectory Selections in the top toolbar. The input data for a sub-orbital trajectory and the resulting plot of the trajectory are illustrated below. This analysis includes the ability to determine time of flight (T) for sub-orbital and orbital flights (e<1). For hyperbolic and parabolic interplanetary flights (e=1 or e >1) the Flight time from burnout to destination orbit (T) represents the flight time in days or years to intersect the orbit of the planet selected using the Destination Planet orbit pull-down menu.
Figure-2, Example of sub-orbital flight.
Heliocentric and Hohmann Transfer Analyses Back
Transfer orbits from Earth to most of the planets in the solar system may be considered to be elliptical and co-planar. For example, a Hohmann Transfer between Earth and Mars may be achieved when the elliptical transfer orbit is tangent to Earth’s orbit at departure (v1=0 deg) and tangent to Mars orbit at arrival (v2=180 deg). This kind of interplanetary transfer orbit is called a Hohmann Transfer and represents the minimum delta-velocity (dV) required for Mars orbital insertion from Earth orbit. Other heliocentric (around the Sun) orbits to Mars and the other planets are possible if the transfer orbit intersects both the origin planet orbit and the destination planet orbit.
For example, when traveling from Earth to Mars the following Hohmann Transfer is possible. SpaceTravel results for Time of flight from burnout to intercept to Mars from Earth is 258.93 days with an Orbital Velocity around the Sun at burnout of 32.729 km/sec and dV for transfer orbit insertion is 2.945 km/sec for orbital insertion. Please see page 365 of Fundamentals of Astrodynamics or Table-1 for similar results from that reference.
Figure-3, Example of Hohmann transfer from Earth to Mars.
Solar System Calculator Back
The Solar System Calculator animates the orbital motion of the planets around the Sun. By checking the Solar System check box a present-day display of the solar system appears in the plot area to the right. Positions of the planets in the solar system as of the date and time displayed in green appears in the orbital plot. By specifying the desired time in the Maximum time from present input box the user can animate motion of the planets around the Sun. Also, by clicking the STOP command button the user can “freeze” the planet positions prior to reaching the maximum time specified. Finally, the ZOOM slider bar is used to zoom-in and zoom-out of the solar system plot.
Figure-4, Solar System calculations.
Asteroid 11600 Cipolla orbit determined by JPL/NASA using 2-body method.
Variable Specific Impulse Magnetoplasma Rocket Analyses Back
A VASIMR plasma rocket motor is capable of varying specific impulse, thrust and exhaust velocity while maintaining constant power. For a VASIMR powered vehicle being accelerated in space, thrust decreases and specific impulse (Isp) increases while the ship accelerates to maximum velocity. For a VASIMR engine, exhaust power is kept maximum allowing thrust and Isp to be inversely related. Therefore, increasing thrust (or Isp) always comes at the expense of Isp (or thrust). For the same propellant, a rocket with a high Isp delivers a greater payload than a rocket with a low Isp but over a longer period of time. However, if a rocket could vary thrust and Isp during acceleration then propellant usage can be optimized allowing the rocket to deliver a maximum payload in minimum time. Therefore, unlike standard rocket motors, VASIMR can by increasing its plasma exhaust temperature, boost specific impulse while reducing fuel consumption (mass flow rate) while at the same time reducing thrust for optimized operation. When this process is 100% efficient the ship is moving at the exhaust velocity allowing all the energy in the exhaust to be transferred to the ship. Initially, the ship accelerates at high thrust and low Isp but as speed increases the thrust gradually decreases and Isp gradually increases for better fuel economy.
For example, by using the Interplanetary Transfer Orbit From Earth analysis screen (see Figure-3) a general heliocentric transfer orbit from Earth to Mars in 39.66 days can be calculated. By inputting True Anamoly at origin planet (Earth) equal to 58 degrees and True Anamoly at destination planet (Mars) equal to 90 degrees the orbital results are included in a plasma rocket powered trajectory analysis after the VASIMR Analysis command button is clicked in the top menu of the StarTravel screen. Figure-5 presents the StarTravel results for a VASIMR powered trip to Mars. Please see the MathCAD VASIMR analysis where some of the equations required for this analysis are applied.
A StarTravel VASIMR analysis will determine time of flight, coast time, distance traveled during powered flight, distance traveled during coast, propellant mass required, mass fraction, velocity increment (dV) during powered flight, velocity at start and end of powered flight, specific impulse at start and end of powered flight, acceleration at start and end of powered flight, and finally thrust at start and end of powered flight. The user can plot thrust verses time, mass flow rate verses time, velocity verses time, distance traveled verses time, specific impulse verses time, mass flow rate verses exhaust velocity, thrust verses exhaust velocity, rocket acceleration (Gs) verses time, rocket mass verses time, trajectory from Earth to destination planet and finally a detailed VASIMR drawing with component descriptions. NOTE: A StarTravel VASIMR analysis can also analyze nuclear rocket powered flights to the planets simply by specifying specific impulse (Isp) and total power as constant.
Figure-5, Example of VASIMR heliocentric transfer orbit analysis from Earth to Mars.
Relativistic Interstellar Travel Analysis- Star Travel near the speed of light (C) Back
It is impossible to exceed the speed of light because as an object approaches the speed of light the inertial mass of an object and therefore its mass approach infinity. It would take infinite power to accelerate an object beyond the Einstein limit (C) or “light barrier”. However, because of time dilation as predicted by Einstein's theory of Relativity, an astronaut can travel stellar distances, that is many light years (ly) within his/her own life time while many thousands of years will have elapsed on the planet of departure or Earth in our case.
For example, if a starship leaves the vicinity of Earth with a constant acceleration of 0.999998G’s toward a star located 1000 ly (light-years) from Earth. Determine (a) the elapsed time on Earth when the starship reaches the star and (b) the proper time on the ship, relative to Earth clocks. From the Relativistic Interstellar Travel screen the results are: a) Elapsed time on Earth during the flight is 1002.65 years. b) Elapsed time on the starship (proper time) during the flight is 13.46 years.
Figure-6 Relativistic Time Dilation and Doppler light shift analysis showing FWD (forward) star colors.
Satellite Trajectory Kit Analysis
The Satellite Trajectory Kit routine in StarTravel solves the basic equations of rocket motion using a finite difference procedure for predicting velocity, altitude and acceleration of ballistic missiles and rockets. Prior to performing a rocket flight simulation the drag coefficient, Cd verses Mach number curve must first be created and saved using the AeroRocket program, AeroDRAG & Flight Simulation. The program allows Cd to vary with Mach number for high speed and high altitude flight analyses. Once a few simple rocket specifications are defined, the program automatically calculates altitude at burnout, range at burnout, velocity at burnout, Cd at burnout, maximum altitude, time from liftoff to apogee, time from liftoff to perigee, maximum range (suborbital) and time from liftoff to impact (suborbital) for single and two stage rockets and whether the rocket can achieve orbital velocity. Satellite Trajectory Kit performs a two step roll maneuver for orbital insertion by specifying the initial flight path angle, flight path angle at insertion, time from lift-off to roll initiation and time from lift-off to flight path angle insertion. A linear variation of roll angle verses time is assumed during the pre-programmed roll maneuver for orbital or suborbital ballistic trajectory insertion.. For hypersonic aircraft and lifting bodies like the X-30 the ability to specify lift to drag ratio (L/D) is included for determining overall flight performance. The following sample analyses are included during program installation in the WinZip file, Trajectory_Projects.pdf. Xcor Lynx Mark II, X-30 NASP, V-2 Rocket, Atlas-5 RD-180 2-Stage Rocket, 1-stage surface to surface rocket and a high power rocket.
Figure-7 Satellite Trajectory Kit analysis of the Atlas-5-400 two-stage rocket powered by the RD-180 rocket motor.
Figure-8 Satellite Trajectory Kit analysis of the X-30 NASP hypersonic spaceplane powered by SCRAM jet propulsion.
THEORY USED IN
SATELLITE TRAJECTORY KIT
The basic equations of rocket motion are obtained from Newton's First Law of Motion, SF = ma. Where, SF is the summation of all external forces applied to the rocket, m is the mass of the rocket and a is the acceleration of the rocket. Acceleration is also expressed as dV/dt or the rate of change of velocity with respect to time. The forces acting on a rocket during the thrusting phase of flight are its weight (W), thrust (T), and aerodynamic drag (D = Cd * 1/2 * r * V^2 * A). Where Cd is the drag coefficient, r is the air density, V is the velocity and A is the reference area of the rocket, typically the maximum cross sectional area of the rocket. However, during the coasting phase of flight forces acting on the rocket are its weight (W) and aerodynamic drag (D = Cd * 1/2 * r * V^2 * A) and T (Thrust) = 0 because the rocket motor is no longer operational. For simplicity, Newton's equation of motion for the thrusting phase of flight becomes: dV/dt = T/m - Cd * 1/2 * r * V^2 * A/m - g *sin(q). The following equation is derived for the term, dV/Dt, Notice that m = W/g in the equation of motion. The acceleration term, dV/dt determines the added (+/-) increment of velocity at the end of each time step (dt) during the flight integration process where dV = dV/dt * dt is the incremental velocity. Velocity (V) and altitude (Sy) at the (n+1)'th time level are determined from the following equations knowing the velocity and altitude at the previous or n'th time level. Typically, the initial thrusting boundary conditions are V(1) = 0.0 and Sx(1) = 0.0, Sy(1) = 0.0 at t = 0. The equations of motion are integrated by performing the analysis at time step, dt. These equations can be integrated using a variety of techniques including the Euler method or ordinary time stepping. For additional accuracy the user may increase the number of time steps (dt) in increments of 100 to a maximum of 10,000 time steps and then plot the residuals to determine if convergence has occurred.
Summary of Basic StarTravelTM
MODIFICATIONS AND REVISIONS
StarTravel 18.104.22.168 Modifications (10/07/2012) NEW!
Developed a Variable Specific Impulse Magnetoplasma Rocket (VASIMR) analysis or a standard constant specific impulse rocket analysis by simply specifying starting Isp and ending Isp or constant Isp for heliocentric flight to planets and stars.
StarTravel 22.214.171.124 Modifications (01/29/2012) NEW!
Developed Satellite Trajectory Kit to determine the ballistic trajectory of rockets and missiles launched vertically, horizontally and everything in between.
StarTravel 126.96.36.199 Modifications (09/15/2009)
1) For StarTravel, fixed all input data text boxes for 32 bit and 64 bit Windows Vista and Windows 7. When operating earlier versions of StarTravel in Windows Vista the input data text boxes failed to show their borders making it difficult to separate each input data field from adjacent input data fields.
StarTravel 188.8.131.52 Modifications
1) For the Heliocentric and Hohmann Transfer Analyses and the Solar System Calculator the central Sun image has been replaced by a realistic image of the Sun.
StarTravel 184.108.40.206 Modifications
1) During a Solar System animation each planet's starting point location in orbit is marked by a hollow white circle.
2) After each Solar System animation the option, Planetary-plots appears. This option allows the X-Y plot of Planet velocity vs. true anomaly, Planet velocity vs. elapsed time, Angular momentum (h) vs. true anomaly and Angular momentum (h) vs. elapsed time. Where, angular momentum, h = 2 dA/dT is constant for each planet's orbit in agreement with Kepler's second law of planetary motion. Kepler's second law states "The line joining the planet to the sun sweeps out equal areas in equal times" or another words, dA/dT = constant.
3) Fixed the plot position error for the dwarf planet Pluto which becomes appreciable for elapsed time approaching 100 years. For purchasers of StarTravel 3.0 please contact AeroRocket to receive your FREE upgrade to the new version which fixes this error.
StarTravel 220.127.116.11 Modifications
1) The Solar System Calculator now uses an iterative solution based on Kepler's second law that states "The line joining the planet to the sun sweeps out equal areas in equal times" to compute planetary positions verses time.
2) Easily reset the Solar System Calculator to its initial starting screen by clicking the T=0 command button.
3) New version 3 screen images included in the detailed instructions, StarTravelManual.pdf.
Minimum System Requirements
(1) Screen resolution: 800 X 600
(2) System: Windows 98, XP, Vista, Windows 7 (32 bit and 64 bit), NT or Mac with emulation
(3) Processor Speed: Pentium 3 or 4
(4) Memory: 64 MB RAM
(5) English (United States) Language
(6) 256 colors
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Note: This web page is intended to describe the astrodynamics program, StarTravel and is NOT an instruction manual. The complete 20 page instruction manual is included in the program installation and is called StarTravelManual.pdf. Upon installation, StarTravelManual.pdf may be accessed from the main screen and is located in the StarTravel folder. For more information about StarTravel please contact AeroRocket.
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