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Planet Simulation is a Dan-Ball game which simulates planets' universal gravitation released on April 2006. On 29th May, 2015 the game received HTML5 support, the third title to do so after Font Game and Liquid Webtoy.

Planet Simulation

This shows Planet Simulation in action.

Screen[]

Left-clicking on the screen performs the action specified by the current Tool. Right-click has no effect. The status bar displays the following information:

  • S, M, L - Count of Small, Medium, and Large objects currently in the simulation.
  • SUM - Total object count, including Stars.

Tools[]

In addition to the tools listed, the tool area has four blank spots which can be selected but have no effect.

Color[]

Changes the colour of objects released. Select "?" for random colors. On the iPhone version of the game, the color yellow with a large planet has rings around it like Saturn. This does not occur on the online version.

Track[]

Changes track left from an object. Options are Line (the default), Long Line, Point (a series of dots), and Non (None).

Target[]

Places an object in the simulation with a specified direction and speed. Click the starting point, and drag to set trajectory. Red line indicates initial velocity and points in direction of travel. Release to start the object moving. Of course, the actual path will depend on the gravitational force of other objects in the simulation.

Random[]

Places objects with random trajectories into the simulation. The number (1-5) indicates the velocity of the objects released. Hold down the mouse to continuously release objects.

Circle[]

Places an object in the simulation with a direction and speed that will put it in a circular orbit around the nearest Star. Note that the orbit will be disturbed by the gravitational force of other objects. This option is not available in the iPhone version.

Size[]

Changes size of objects placed in simulation. Sizes are S(mall), M(edium), and L(arge). These objects interact gravitationally and can also collide with each other. In terms of the mass of the large object, the masses are

  • Star: 10
  • Large: 1
  • Medium: 0.01
  • Small: 0.001

(See the Physics section.) When two objects collide, the results depend on their relative size. If one object is larger, then the smaller object simply disappears. Note that mass is lost in this case; objects do not accrete mass. The large object's trajectory is also changed slightly, if the smaller object is made up of many small objects put in the same place the change in trajectory would be very large.

If the objects are both Large, then both objects shatter and six Small objects are generated from each. Their velocity and direction are roughly equivalent to those of the parent objects, with a little bit of random scatter.

If the objects are both Medium, then both objects shatter and three Small objects are generated from each.

If the objects are both Small then they pass each other; they do not collide. This allows multiple small masses to be put in the same place, acting like a denser object of the same size.

Summary:

  • 2 Medium -> 6 Small
  • 2 Large -> 12 Small
  • 2 Small -> 2 Small

Based on the known masses of the three types of objects, mass is not conserved in the collisions.

Star[]

Creates another star, which is a high gravity point similar to the black hole in Earth Editor. Stars do not move relative to the viewer, or to each other. Anything that falls into a star is absorbed (again, its mass is lost). To remove a star, select the star tool and click an existing star.

Scale[]

Scales in and out from the screen. A scale of 1 corresponds to approximately 2 AU (Astronomical Units, compared to the default yellow star and blue object).

Speed[]

Toggles speed of action. In addition to 0 (all stop) and 8 (very fast), this simulation includes 1/2 and 1/4 speed.

Reset[]

Resets game field to one Large blue object around one yellow star.

Physics[]

The planet simulation uses Newton's inverse square law for gravity, which is exactly what describes gravity in the real world. The force between two masses and separated by distance is

,

where is Newton's constant. The simulation uses a much larger value of than in the real world so that objects don't take years to orbit a star.

Relative Masses[]

The relative masses of the objects used in the simulation can be determined by releasing pairs of objects and measuring the time until collision.[1] Using Newton's law of gravitation and the conservation of energy, one may derive

,

where and are the masses of the objects and is the original separation. If one of the masses is a star, which does not move, then only the mass of the star will appear in the denominator, not the planet. The overall length and mass scales of the simulation are somewhat arbitrary, but doing the same experiment for different pairs of masses still determines the mass ratios, since and are the same in each case.

Value of G[]

An object in a circular orbit around a fixed mass has period

,

where is the radius of the orbit.

The default planet takes almost exactly 12 seconds to complete one orbit. If we take the mass of the star to be 10 (as in the table in a previous section) and the default radius to be 1 unit, then the circular orbit equation requires

.

This value, the values of the masses, and the laws of orbital mechanics fully control the simulation.

Interesting scenarios[]

Some examples of interesting scenarios which can be created in Planet Simulation are:

  • Create a small moon in orbit around a large planet, while it orbits a sun.
  • Create a binary star system and send a planet into an eight-shaped loop around it.
  • Observe various details of orbital mechanics, for instance, orbital precession.

History[]

Version Date Thumbnail New features and changes Blog[2]
2.2 26/05/2023 PS ver2.2 Full Screen support. jp/en
2.1 01/10/2021 PS ver2.1 The game now supports resizing in mobile browsers. jp/en
2.0 15/06/2018 PS ver2.0 Bug fix (Scrolling while playing the game on smartphones). jp/en
1.9 15/07/2016 PS ver1.9 Optimization (60 FPS, Font). jp/en
1.8 29/05/2015 PS ver1.8 HTML5 Support. jp/en
1.7 04/02/2007 Tool addition (Speed). jp/en
1.6 26/11/2006 Tool addition (Circle). jp/en
1.5 30/07/2006 Game dimensions increased. jp/en
1.4 10/07/2006 Star addition. jp/en
1.3 09/05/2006 Scale changes. Objects are deleted if they leave the border. jp/en
1.2 03/05/2006 Random added to colour selection. Planet collision mechanism added. jp/en
1.1 25/04/2006 Tool addition (Track and Random). jp/en
1.0 20/04/2006 Game creation. jp/en
  1. An experiment to determine the relative masses can be set up as follows: First, remove all objects. (Start the default simulation and destroy the planet by creating a new star on top of it. Then delete both stars.) Set the simulation speed to 0. Place an object as close as possible to one corner, and place another at the diagonally opposite corner. Then unpause the simulation and start a timer. If you right click on the speed, it will go directly from 0 to 8. This helps when using small masses, for example, since the collision time is very long. Stop the timer exactly when the masses collide. Multiply the measured time by whatever speed factor you used, and record this.
  2. The original blog is written in Japanese. A link to an automatic translation into English by Google is also available.

External links[]

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