
StarTravel^{TM}
Features
Circular, Elliptical and Parabolic/Hyperbolic Orbital Analysis
Go
1) Plot Suborbital, orbital and escape trajectories around planets in the solar
system knowing Burnout velocity (Vbo) and Flightpath angle at burnout (f).
2) Determine distance traveled from liftoff to impact (X) along planet curvature
and suborbital flight path knowing Maximum altitude at burnout (Hb) and Down
range distance at burnout (Xb).
3) Free flight angle
from liftoff to impact (y), Suborbital 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) Zoomin to see nearplanet 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 (V_{00})
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 accelerationvelocity 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 Gloading 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 6.4.0.5 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.
Suborbital,
Orbital and Escape Trajectory Analyses
Back
As illustrated
in Figure1 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 twobody
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).
Figure1, Conic sections defined
by eccentricity (e) and the other orbital elements.
To perform
suborbital, orbital and escape trajectory analyses click Suborbital, orbital
and escape trajectory under Trajectory Selections in the top toolbar.
The input data for a suborbital trajectory and the resulting plot of the
trajectory are illustrated below. This analysis includes the
ability to determine time of flight (T) for suborbital 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 pulldown menu.
Figure2, Example of suborbital
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 coplanar. 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 deltavelocity (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
Table1 for similar results from that reference.
Figure3,
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 presentday 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 zoomin and zoomout of the solar system plot.
Figure4, Solar System
calculations.
Asteroid 11600
Cipolla orbit determined by JPL/NASA using 2body 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
Figure3) 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. Figure5 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.
Figure5,
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 (lightyears) 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.
Figure6
Relativistic Time Dilation and Doppler light shift analysis showing FWD
(forward) star colors.
Satellite Trajectory Kit Analysis
Back
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 liftoff to roll
initiation and time from liftoff to flight path angle insertion. A linear
variation of roll angle verses time is assumed during the preprogrammed roll
maneuver for orbital or suborbital ballistic trajectory insertion.. For
hypersonic aircraft and lifting bodies like the X30 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, X30 NASP, V2 Rocket,
Atlas5 RD180 2Stage Rocket, 1stage surface to surface rocket and a high
power rocket.
Figure7 Satellite
Trajectory Kit analysis of the Atlas5400 twostage rocket powered by the
RD180 rocket motor.
Figure8 Satellite
Trajectory Kit analysis of the X30 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 StarTravel^{TM}
Features
MODIFICATIONS AND REVISIONS
StarTravel 3.0.0.9 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 3.0.0.8 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 3.0.0.7 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 3.0.0.6 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 3.0.0.5 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, Planetaryplots appears.
This option allows the XY 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 3.0.0.1 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.
StarTravel
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 Please note this web page requires your browser to have Symbol fonts to properly display Greek letters (a, m, p, ∂ and w) 
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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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