Joachim Köppen Kiel/Strasbourg/Illkirch November 2010


About the Applet and what it does

The PlanetTraveller Applet computes and displays the orbit of a body around the Sun. This can be a planet, an asteroid, a comet, a chunk of rock that may collide with the Earth, or a spacecraft sent off from Earth into interplanetary space. The orbit is treated as a simple Keplerian orbit around the Sun, thus we neglect the perturbations by all the other bodies in the Solar system. We also neglect any inclination of the orbit against the plane of the Earth orbit. This is sufficient for getting a first idea. And as long as we are not interested in the positions after many orbits or the exact close approach to the target planet, this is a fair approximation.

The applet comes in several versions, which offer features convenient for various problems. They are

In these pages, the various features of the applets are described. As we shall use the version which has all features, you will find that some may not be present in the version you are working with.

Let's take first steps

When you start up the applet, you would see something like the following screen:

On the left hand side there is a number of fields to enter the position and velocity data of the target body at time 0.0; below are shown the properties of the orbit. The right hand side gives a view of the Solar System as seen from a point above the Ecliptic plane, showing the orbits of the planets: Here we selected the major planets only, and we had already clicked drag & zoom and dragged a small rectangle to concentrate on the inner part. The Earth and all the planets move around the Sun in counter-clockwise sense. The target body's orbit is shown in red, the green dot marks its position at time 0.0 - which means here the time of the collision with Earth (whose orbit is blue). The thicker parts of the red curve indicate the positions at which the body is seen from the Earth with both brightness and proper motion sufficiently large to be detected (for these detection limits see below). The grey orbit is that of the "manual interceptor": here it had been designed to intercept with the target body at the small red circle (see below).

On the top there are several buttons to perform the navigation between the various pages of the Applet. Please note that these buttons differ in the various versions. Right now, we are on the Target Orbit page, which lists the relevant parameters:

here you may enter the distance from the Sun where the collision (or the launch) would take place. Collisions with Earth are of course at 1 astronomical unit [AU]
Body's Helioc.Phase
this tells merely on which side of the plot the body is placed at time zero: 0 degrees is to the right of the Sun ("East"), 90 degrees refers to "North", 180 degrees to "West". This changes only the orientation of the orbit, not its shape
Earth's Helioc.Phase
this is the position of the Earth at time zero. For a collision or a launch, one makes it equal to the Body's phase (this additional feature gives a greater flexibility).
is the speed of the body at launch or collision time, but with respect to the Sun
is the direction of the heliocentric velocity vector with respect to the direction of the movement of the Earth: 0 degrees is in the same direction, 90 degrees is straight away from the Sun, 180 degrees is against the Earth movement (as in a head-on collision) and -90 or 270 degrees is pointing right into the Sun
To change any parameter, click on the text field, modify or enter the value, and then hit the Return or Enter key. This will cause any plot to be redrawn with the new situation, and any displays to be updated.

The characteristics of the orbit are displayed as

Semi-major axis
is given in AU. This has a physical meaning only for elliptical orbits
with 0 meaning a circular orbit, 1 either parabolic or radial orbit, and larger than 1 for hyperbolic ones
Orbital period
is given in years, if the orbit is elliptical
is the largest distance from the Sun
is the cloest approach to the Sun
The orbit shown here is similar to that of an asteroid; in the PlanetTraveller applet we start with a comet like Halley's, in Jupiter applet we use that planet, of course. By entering other launch parameters you can modify the target's orbit to your needs.

On the right hand side we saw the plot of the orbits in the Ecliptical Plane. But there are other plots:

Radius displays the distance of the target body from the Sun as a function of time by a red curve. The horizontal lines indicate the major planets. We see that this body passes the Earth orbit every 8.4 years, and that at the instant marked with a green line (time = -1.0, i.e. one year before the collision) the body was 4 AU from the Sun and 4.6 AU from the Earth, as seen on the View page on the left hand side. Note that here we enter the time for the green mark, and that this instant is marked in the plane plot with the small red circle. The grey curve is the distance of our interceptor, where we can identify the launch from Earth and the meeting with the target.

Next we can plot the Distance from Earth as a function of time. We see the yearly oscillation because of the Earth movement. Again, the grey curve shows the progress of our interceptor.

As a result of the varying distance the brightness Magnitude of the body as seen from Earth changes. Evidently it becomes very bright prior to its collision. [Please note that in the Jupiter version, this magnitude is NOT computed]

On the left hand side, we now have the Target Properties page: it contains input and output fields related to the properties of the body and to its detection:

is the fraction of how much light the target body is able to reflect
this is a Choice to select the albedo among various materials and the planets. Chose any and its albedo is displayed in the text field and taken into account in the computations of the brightness
here one can enter the density of the body, which is used to compute the mass and the impact energy
this Choice is for selecting a density typical for meteoroids and comets. This datum is only used for the density, it does not affect the albedo
of the body. In all the calculations we shall assume it is of spherical shape
Limiting magnitude
this is the visual magnitude which sets the lower limit for detection
this is the threshold for the detection of the body due to its motion across the sky. It is indicated in the plot at the green horizontal line. In the view of the ecliptical plane, the target's trajectory is shown thicker whenever the body appears brighter than this threshold value

The Radial Velocity is shown. Red curves indicate the body moving away from us (redshift), blue curves that it moves towards us.

On the left hand side, we went to the Earth page: . It tells about the conditions at collision time (such as: the speed with respect to Earth (this takes into account the orbital speed of the Earth), the velocity change that would be necessary to either place the incoming body into a low Earth orbit, or to insert a space probe from its parking orbit into the red trajectory. Furthermore, it gives the speed of the impact (which takes into account the gravitational attraction of the Earth), and the resultant impact energy (in Megatons of TNT). We also list estimates for the resulting crater size and measures of the devastation from the impact. The formulae are taken from the JavaScript utility by A.Goddard based on formulae by Eugene Shoemaker.

Finally, we also show the Proper Motion which is the apparent movement of the body seen in the sky from Earth. This motion is larger than that of the stars and it thus serves as an indicator of a close-by object, and is useful for the detection of these bodies.

The Manual Interceptor allows to launch a space probe, for instance to meet the target body at some position or some time before its collision with Earth.

The page on the left has these input fields

launch time
is when the probe leaves Earth. This time is given in units of years, and relative to time zero, at which the flight parameters of the target are specified
is fixed to 1
is fixed by the position of the Earth at the time of launch
the speed at insertion into interplanetary orbit
the direction into which the interceptor is inserted
Here you also find a button to show/hide the interceptor's orbit in the plot.
At lower left, the characteristics of the resulting orbit are listed.
After a bit of practise, you'll find it quite easy to adjust the parameters so that you get the desired orbit!

If you want the spacecraft to meet the target at a certain time, enter this time on the View page so that the positions of the target and the interceptor are marked with the small red circles. All you need to do is then to fiddle with the insertion parameters until the two circles meet.

In the example shown, the probe was launched at t=-2.9 from Earth - the spot is NOT specifially marked. The green dot marks when it would be at time=0 (collision time). It meets the target at t=-1, marked by red circle.

There are two more buttons in the upper right: Refresh simply redraws the plot, in case of need. single curve/over allows to overplot several curves, for instance if one wants to compare the curves from two different orbits for the target body or for the manual interceptor ...

The Depart/Arrive page: Two versions have the blue button which gives access to the page on the left:

This rather complex page is used in a number of ways to find the trajectory of a voyage from the Earth to the target body at some times of departure and arrival:

Let us describe each option in detail:

For searching the orbit for fixed departure/arrival times we first enter "0" in the left-most fields, the departure and arrival times in the central fields, and then click the button find Traj..

If a trajectory could be found, the input field now are marked green, the times are also displayed at lower left, and at the tight hand side, the trajectory for this voyage is shown as a magenta curve. The departure is marked with a cyan dot, the arrival with a black dot.

If you want to see the entire orbit, click on Transit path/Full orbit:

Having found a trajectory, you can also inspect the details of the mission by using one of the plot. For instance, how the distance varies with time:

Vertical lines mark the departure (cyan), arrival (black), and our time mark (green). A grey curve would be shown for the manual interceptor, but to avoid cluttering up this plot, we had clicked the hide button. The magenta curve shows that during this voyage the distance varies, because of the spacecraft moving away from the Earth, but also due to the Earth orbiting the Sun. This would be of importance to know, if we have to schedule the communications link to the craft. [A further aspect would be that during some time the Sun would be between the spacecraft and Earth, which would cause a communications blackout!]

Furthermore, the buttons at lower left Depart, Orbit, Arrival, Deflect give access to pages with the numerical values, for instance the situation at arrival:

Click the blue button Dep/Arr to regain access to all other pages.

We can systematically search for suitable voyages in a range of times by entering

If we wait until the scan is finshed, we get a complete overview of the possible trajectories:

Here, the white regions are hyperbolic orbits, red are highly elliptic ones, and the light blue area comprises trajectories between Earth and the target which have minimum eccentricity, i.e. close to Hohmann type ellipses. Some remaining black squares indicate departure/arrival times where the search routine did not find the solution; a finer search would reduce their number but would also be more time-consuming. In the applet, some compromise was taken.

To pick a certain voyage we first click on the button Click&Show Traj. and then click on the map at the point we are interested in. The plot of the ecliptical plane is shown with the orbit of this particular voyage:

The cyan and black dots indicate the positions of Earth and the target at departure and arrival times. Note that in this screenshot the red circles (which mark the time= -1) show that for this mission the target and the spacecraft will not be in the same place ... as shown at lower left, arrival time is -0.673, a few months later! The details of the voyage will be accessible from the buttons at lower left Depart, Orbit, Arrival, and Deflect (for the NEO version).

Once we have done a complete (or even partial) scan of the times, we can now show the characteristics of these orbits, for example the velocity change necessary to launch this spacecraft from low earth orbit (LEO):

As can be seen, the mission we had picked - marked with a small black cross - is quite close to the minimum value for this velocity!

If you click on the map, the coordinates X,Y,Z will be displayed, that is: departure and arrival times and the value of the map found for these particular times. Here, we read that the velocity change from LEO is only 5.5 km/s. Any clicked point is marked by a single white pixel.

Finally, we may zoom in the map but only to prepare the next scan! Click on drag & zoom and then drag the mouse over the rectangular area which you like to explore in more detail. The chosen rectangle is painted in the map, and the new ranges for departure and arrival time appear in the appropriate fields.

If you are not satisfied with that, a click on unZoom brings back the initial ranges, and you may try again (I choose not to go to the trouble to remove the selected rectangle!) Only when you click on Start Scan the new map will be displayed, but please note that now the previous range values are no longer present. If you want to go back to the old map, you have to enter the range values yourself and make another scan.

The Plots and Maps

Here is a list of all the graphical displays available:

XY View
the view of the ecliptical plane
distance from Sun
distance from Earth
target's brightness as seen from Earth
radial velocity
target's radial speed as seen from Earth
proper motion
target's proper motion as seen from Earth

depart speed
spacecraft's heliocentric speed at departure from Earth
depart direction
its heliocentric direction
dep.speed (Earth)
its speed with respect to Earth (Earth)
its direction with respect to Earth
DeltaV from LEO
velocity change necessary when launched from low Earth orbit

semi-major axis of spacecraft's orbit
its eccentricity
its period
the number of complete orbits necessary for the trip

arrival distance
target's distance at arrival
its brightness at that time
spacecraft's speed with respect to the target
its direction as seen by the target
body prop.motion
target's proper motion at arrival
body rad.speed
its radial velocity

sidew. DeltaV
change of velocity of the target, if one wants to prevent the collision with Earth by giving the target a push perpendicular to its present flight direction. A deflection of the distance Earth/Moon is assumed.
sidew. DeltaE
the amount of energy necessary for that
forwd. DeltaV
change of velocity, but for a push in direction of target's present flight path
forwd. DeltaE
the energy needed for that

Some Computational Details

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last update: 10 Nov. 2010 J.Köppen