Version 1.1 Demo

User's Guide

Acknowledgments

Introduction

About Newton's Aquarium

About Eureka Software

Ordering Information

Getting Started

System Requirements

Installation

Loading

Tutorial

Working With Sample Universes

My First Universe

Reference

Universe Documents

Menus and Toolbars

Windows and Dialogs

Appendix

Keyboard Shortcuts

Glossary

Acknowledgments

First and foremost, I would like to thank my co-author and close personal friend Kiran Arora for donating her valuable time and skills. Without her contribution, this project would not have been possible. Thanks also to Dave Charlesworth, and his son Ian, for playing with 1.0 as much as they did. Their feedback and enthusiasm was very encouraging. Thanks to Bill Lucas for putting up with so many nit-picky questions. His common sense and intuition has helped to shape this software in many ways. And finally, thanks to Peter Zion for helping us with our numerical methods. Now we can be a whole lot more certain about the fate of the universe!

Shawn Leclaire
Dec. '98

Introduction

About Newton's Aquarium

Developing an intuition for the motion of heavenly bodies is a challenge for even the best of students. The problem is that human beings do not directly experience celestial motion. For many of our daily observations we treat the Earth like a fixed point in space. Our ancient ancestors even went so far as to create entire religions around the notion of an Earth centred universe, a notion that stayed with us for thousands of years.

Quantifying celestial motion in terms of Newton's Law of Universal Gravitation is a greater challenge still. Newton's inverse square law only describes the gravitational force acting between two bodies. Several steps of algebra and geometry and dozens of calculations are necessary to determine the path of just a single planet. The motion of an entire solar system would take days to work out by hand.

As a result, orbital mechanics is often overlooked in introductory physics studies. This is unfortunate, as orbital mechanics is perhaps one of the best demonstrations of classical physics. Everything from centripetal acceleration to conservation of momentum to Newton's three laws of motion can be seen at play. With the advent of powerful desktop computers, it is now possible to explore the heavens as never before...

Newton's Aquarium is a solar system construction set that allows students to create and explore situations involving any number of stars, planets, moons and asteroids. The software uses an interactive, visual approach to physics. The hope is that with Newton's Aquarium, students will develop an intuition for orbital mechanics. In addition, students will gain a better understanding of the physics behind the images. While creating and exploring their own solar systems, students are exposed to many of the core concepts in kinematics and dynamics.

Newton's Aquarium was designed for use in high school and college physics studies. The software offers interactive 3-D n-body simulation, display of velocity, acceleration and force vectors, collisions, centre of mass and conservation of momentum, variable G and distance exponent and actual mks units. On-line help, lesson plans and student activities are provided to help teachers integrate the software into existing curriculum.

With Newton's Aquarium, students can now explore the motion of heavenly bodies using only their computer, a point-and-click interface and their imagination.

About Eureka Software

Eureka Software Inc. was established in 1994 in Kingston, Ontario, Canada to develop and publish educational software. The company was formed to meet the growing need for new and alternative approaches to math and science education. Eureka has succeeded by creating interactive software products that help students visualize and understand scientific concepts.

Eureka offers physics students an interactive look at Newton's Law of Universal Gravitation with its flagship product Newton's Aquarium: A Solar System Construction Set. While creating and exploring their own solar systems, students are exposed to many of the core concepts in classical physics. With Newton's Aquarium, students develop an intuitive understanding of the laws governing our universe.

Students studying chemistry can say good-bye to flat blackboard sketches and diagrams with VSEPRplex: An Introduction to Molecular Modelling. Like Newton's Aquarium, VSEPRplex (pronounced "ves-per-plex") uses a point-and-click interface and interactive 3-D graphics to help students explore the shapes of small covalent molecules. With VSEPRplex, students are better able to visualize the fundamental shapes that give rise to more complex structures.

All of Eureka's products give students the opportunity for discovery through hands-on exploration. Our interactive and visual approach complements more traditional methods to cement students' understanding of difficult concepts.

Eureka is striving to provide new and innovative ways of teaching math and science by creating powerful simulation and visualization tools. As a result of its ongoing commitment to education, Eureka has become an important part of classrooms around the world.

Eureka Software Inc., 110 Bagot Street, Kingston, Ontario, Canada K7L 3E5
Voice: (613) 546-4818, E-mail: info@eureka.ca, Web: www.eureka.ca

Retail Price List and Ordering Information

Newton's Aquarium is available for Mac OS.

High School, College, University or Other Institution

Limited Site Licence. Purchasing department of the institution may install and use the software on "X many" computers within the department.

PRICE = $100 US / $125 CDN for first copy + $20 US / $25 CDN for each additional copy.

Unlimited Site Licence. Purchasing department of the institution may install and use the software on any number of computers within the department.

PRICE = $400 US / $500 CDN.

Any Larger Licence. Example: Purchasing school board may install and use the software on any number of computers in every school within the school board.

PRICE = NEGOTIABLE. Please contact Eureka Software Inc.

Student or Other Individual

Single User Licence. Purchaser may install and use the software on a single computer. This type of licence is intended for students, hobbyists and other "home" users and is not available to institutions.

PRICE = $28 US / $35 CDN.

All prices include shipping and handling costs.

Ontario customers, add 8% to all prices for Provincial Sales Tax. This product is not subject to Canada's Goods and Services Tax.

Your order should specify the type of licence (and, in the case of a Limited Site Licence, the number of copies).

Please make your cheque, money order or purchase order payable to Eureka Software Inc. Send your order to:

Eureka Software Inc.
110 Bagot Street
Kingston, Ontario
Canada K7L 3E5

Thank you for your support.

Getting Started

System Requirements

In order to use the Newton's Aquarium Demo, you will require:

Mac OS 7.0 or later (8.0 or later recommended)
2 MB free memory (3 MB or more preferred)
68020 processor or better (68040 or PowerPC recommended)

Installation

The Newton's Aquarium Demo installation program will copy the necessary files to your hard-disk. To run the installer, do the following. Insert the installation disk (a disk icon will then appear on your desktop). If necessary, double-click the disk icon to open the disk.

Double-click the installer application icon and follow the on-screen instructions.

Loading

Depending on your installation, there may be more than one Newton's Aquarium Demo application to choose from. If you have a PowerPC based Mac, then use the PPC application. If you have a 680x0 based Mac, then you have two choices. If your 680x0 based Mac has a math coprocessor, then use the FPU application. Otherwise, use the 68K application. If you are not sure what type of Mac you have, then, for best performance, try the applications in this order: PPC, FPU, 68K.

Tutorial

Note: If you have not yet installed the Newton's Aquarium Demo (along with the sample documents), please do so now. See the Getting Started section for further details.

The following tutorials are designed to help you quickly become familiar with Newton's Aquarium. We encourage you to jump right in and start playing. All you need to know are the basics of pointing and clicking on your computer.

Working With Sample Universes
My First Universe

The tutorials have you perform several tasks using the menus. If you prefer, feel free to use the toolbars instead.

For detailed information on all features, see the Reference section.

Working With Sample Universes

This tutorial will show you how to open and run the sample universe documents we have provided with Newton's Aquarium. These samples will give you an idea of some of the concepts that can be explored using Newton's Aquarium. As well, the samples will give you a starting point for creating your own universes.

Step 1: Start the Newton's Aquarium Demo. Once the program has loaded, the Open dialog box will be displayed. Use this dialog to locate the sample documents, which live in a folder called Sample Universes. This folder is normally installed in the same place as the application.

Step 2: Select Sun and Earth from the list of documents and click the Open button. Once the the document has loaded a universe window will be displayed. In the window you will see two objects: A yellow star in the middle and a small light blue planet over to the right. You will also see two lines emanating out from the planet. These lines represent the planet's initial velocity (green) and acceleration (blue).

Step 3: Run the simulation forward in time by selecting the Animate Forward item from the Animation menu. The two bodies will then be subjected to Newton's laws of motion and the planet will begin to move. As the planet travels around the star, notice how the planet's acceleration vector always points towards the star.

Step 4: Erase the planet's trail by selecting the Clear Trace item from the Universe menu. Try turning trails off entirely by selecting the Turn Trace Off item.

Step 5: Use the Cursor keys to view different parts of the universe. Try selecting the Zoom In and Zoom Out items from the Universe menu.

Step 6: To stop the simulation, select the Stop item from the Animation menu. To return the universe to its initial conditions, select the Reset item.

Step 7: Close the universe by clicking the Close box at the top-left of the universe window or by selecting the Close Document item from the File menu. Don't bother saving changes.

Step 8: Try out some of the other sample universes. Many have built in student activities to guide you. To exit the program, select the Quit item from the File menu.

My First Universe

This tutorial will show you how to create a universe from scratch.

Step 1: Start the Newton's Aquarium Demo. Once the program has loaded, the Open dialog box will be displayed. Click the Cancel button. A new, untitled, universe window will then appear. A new universe contains no bodies to start with.

Step 2: Create a new star by selecting the Star... item from the New Body sub-menu. The sub-menu is located in the Universe menu. The star's Edit Body dialog box will then be display. All new stars use the Sun's mass and radius as default values. Notice that the position of the star is the origin (0,0,0). Enter a name for the star (e.g., Sun) and then close the dialog box. The Close box is located at the top-left corner of the dialog.

Step 3: Create a new planet by selecting the Planet... item from the New Body sub-menu. New planets use the Earth's mass and radius as default values. As before, name the new body (e.g., Earth). Now, enter a value of 1.5e+8 for the x component of the planet's position. This will place the planet 1.5 x 10^8 km away from the star, which is approximately how far away the Earth is from the Sun in reality.

Step 4: Zoom in three or four times using the Zoom In item from the Universe menu. This will make things a little easier to see.

Step 5: Run the simulation forward in time by selecting the Animate Forward item from the Animation menu. The two bodies will then be subjected to Newton's laws of motion and the planet will begin to move.

Step 6: Since the planet's initial velocity is zero, the planet will accelerate towards the star along a straight line and then collide with the star. To stop the animation and return the universe to its initial conditions, select the Reset item from the Animation menu.

Step 7: Double-click the planet to open its Edit Body dialog box. Change the y component of the planet's velocity to 10 km/s and run the simulation again. The planet no longer travels in a straight line. Try other values such as 20, 30 and 40 km/s. Notice the different orbits that result. In reality, the Earth travels around the Sun with a velocity of approximately 30 km/s.

Step 8: Try changing other properties of the bodies in your universe. You can also edit various aspects of the universe itself using the Edit Universe dialog box. To exit the program, select the Quit item from the File menu.

Reference

This section provides complete details on all features of Newton's Aquarium, including universe documents, menus and toolbars and windows and dialogs. Little emphasis is placed on the overall process of creating and exploring a universe. For an overview of how to create, run and save a simple solar system, see Tutorial: My First Universe.

Universe Documents

Newton's Aquarium stores details about a universe and the bodies it contains in a Universe document. A universe document (or file) corresponds to a universe window. Several universe documents (or windows) can be open at one time, the number of which is only limited by free memory. As well, there is no fixed limit on the number of bodies (i.e., stars, planets, moons and asteroids) that each universe may contain.

Universe documents are created, stored and retrieved using the commands in the File menu. New bodies are created and universe and body attributes are edited using Universe menu commands. Simulations are started and stopped using the Animation menu.

Note: When there is more than one universe open, most universe operations or commands (e.g., adding a new body) are applied to the front-most universe window. Some commands, however, can be applied to all open universe documents by holding down a modifier key when the command is invoked. For further details, see Appendix: Keyboard Shortcuts.

Menus and Toolbars

Newton's Aquarium provides the user with several commands that are used to create and work with universe documents. Most commands can be accessed from one of the following menus:

Apple | File | Edit | Universe | Animation | Window | Help

In addition, several commonly used commands can also be accessed more directly from one several toolbars. Use the Window menu to show and hide various toolbars. Icons are included for menu items (both in the software and in the User's Guide) that have toolbar equivalents.

Apple Menu

The Apple menu contains the About Newton's Aquarium item. When selected, this item opens the About dialog box. This dialog displays general information about Newton's Aquarium, such as the program's version number, release date and licensee.

File Menu

The File menu contains the following items and is used to create, open, close, save, export and print universe documents.

New...
When selected, this item creates a new, untitled, universe document. The new document initially contains no bodies. The position and size of the new universe window is based on the position of the previous front-most window (if any), the position of the toolbars (if visible) and the size of the monitor.

Open...
When selected, this item displays the Open dialog box, which is used to open an existing universe document.

On Mac OS, Newton's Aquarium supports stationery pads. For further details, see Save As... item.

On Mac OS, Newton's Aquarium can import Gravitation Ltd. 4.0 and 5.0 documents using the Open dialog box. Gravitation Ltd. documents are opened into an untitled Newton's Aquarium document and may require minor adjustments for optimal use.

Close Document
When selected, this item closes the front-most universe document. If the document needs to be saved, the Save Changes dialog box will be opened and the user will be asked whether to save changes before the document is closed.

On Mac OS, if the option key is held down while selecting this item, all documents will be closed. The user will be prompted for each document that needs to be saved.

Save
When selected, this item saves changes to the front-most universe document. If the document has never been saved before (i.e., the document is still "untitled"), the Save As... item will be invoked instead.

On Mac OS, if the option key is held down while selecting this item, all unsaved universe documents will be saved. The user will be prompted for any "untitled" document that has not been previously saved.

Save As...
When selected, this item opens the Save dialog box. The user can then save a copy of the front-most universe document with a new name. The newly saved copy then becomes the current document.

On Mac OS, Newton's Aquarium supports stationery pads. A stationery pad is a template that describes the contents of a document. When a stationery pad is opened, a new, untitled document is created and the contents of the stationery pad are copied into the new document, leaving the original file untouched.

Revert
When selected, this item closes the front-most universe without saving changes and then re-opens the universe. This command is useful for opening a document, make changes, discarding the changes and starting again with the original document.

Export...
When selected, this item saves the front-most universe as a picture file. This is useful for exporting images from Newton's Aquarium to paint programs and graphics converters. For example, picture files (or PICTs) can be converted to GIF or JPEG format and then easily placed on a web page.

Page Setup...
When selected, this item opens the Page Setup dialog box. This dialog allows paper size, orientation and other print related settings to be adjusted.

Print...
When selected, this item opens the Print dialog box which allows the user to adjust certain print options, such as number of copies, and then print the front-most universe document.

On Mac OS, if the option key is held down while selecting this item, all universe documents will be printed. The user is prompted with a dialog for each universe.

Quit
When selected, this item exits Newton's Aquarium. Any open universe documents will be automatically closed. The user will be prompted for any documents that need to be saved before closing.

Edit Menu

The Edit menu contains the following items and is used to work with text and graphics on the Clipboard. For further details about the Clipboard, also see Windows and Dialogs: Clipboard Window.

Undo
When selected, this item cancels the last operation (e.g., cutting, pasting, clearing, typing, etc.).

Cut
When selected, this item removes the current selection and stores it on the Clipboard.

Copy
When selected, this item copies the current selection to the Clipboard.

Paste
When selected, this item pastes the contents of the Clipboard at the insertion point (or in place of the current selection).

Clear
When selected, this item deletes the current selection without storing it on the Clipboard.

Select All
When selected, this item selects all objects in the front-most window (e.g., all the bodies in the front-most universe window).

Universe Menu

The Universe menu contains the following items and is used to edit the front-most universe.

New Body (in place of Edit Bodies...)
This item leads to a hierarchical menu that is used to create new bodies in the front-most universe. Body types that can be created include Star, Planet, Moon and Asteroid. Fundamentally, all bodies are the same with respect to the laws of physics. The various bodies types created using this menu differ only in their default mass, radius and appearance settings.

Edit Bodies... (in place of New Body)
When selected, this item opens the Edit Body dialog box for each selected body in the front-most universe. This dialog allows all aspects of a body to be customized.

Edit Universe...
When selected, this item opens the Edit Universe dialog box for the front-most universe. This dialog allows all aspects of a universe to be customized.

Turn Trace On/Off
When selected, this item toggles the trace setting for the front-most universe. When trace is on, bodies can leave a visible trail when a simulation is running. The Trace On setting for individual bodies must also be set. For further details, see Windows and Dialogs: Edit Body Dialog.

Clear Trace
When selected, this item erases all trace lines (or trails) from the front-most universe window.

Show/Hide Velocity Vectors
When selected, this item toggles velocity vectors for the front-most universe. Velocity vectors are represented by line segments drawn from the centre of each body. The Show Velocity Vector setting for individual bodies must also be on. For further details, see Windows and Dialogs: Edit Body Dialog.

Show/Hide Acceleration Vectors
When selected, this item toggles acceleration vectors for the front-most universe. Acceleration vectors are represented by line segments drawn from the centre of each body. The Show Acceleration Vector setting for individual bodies must also be on. For further details, see Windows and Dialogs: Edit Body Dialog.

Show/Hide Force Vectors
When selected, this item toggles force vectors for the front-most universe. Force vectors are represented by line segments drawn from the centre of each body. The Show Force Vector setting for individual bodies must also be on. For further details, see Windows and Dialogs: Edit Body Dialog.

Show/Hide Axes
When selected, this item toggles the axes for the front-most universe. Axes provide a useful frame of reference.

Show/Hide Grid
When selected, this item toggles the grid for the front-most universe. A grid is useful when positioning bodies and also provides a frame of reference.

Show/Hide Centre of Mass
When selected, this item toggles the centre of mass for the front-most universe. The centre of mass is represented by an "x" and shows the overall motion of a system.

Zoom In
When selected, this item zooms in on the front-most universe. As a result, less of the universe will be visible. Note: Trace lines are erased as a side effect of zooming.

Zoom Out
When selected, this item zooms out of the front-most universe. As a result, more of the universe will be visible. Note: Trace lines are erased as a side effect of zooming.

Animation Menu

The Animation menu contains the following items and is used to start, stop and reset gravity simulations.

Plot Rate
This item leads to a hierarchical menu that is used to set the plot rate for the front-most universe. There are five qualitative settings to choose from: Fastest (default), Fast, Medium, Slow and Slowest. The plot rate roughly determines the number of frames per second the computer will try to render. The plot rate is not related to the time step.

Turn Anti-drift On/Off
When selected, this item toggles the anti-drift setting for the front-most universe. When anti-drift is on, the overall momentum of the system during a simulation is set to 0 after each time step. This has the effect of preventing the system from ever "drifting" out of view.

On Mac OS, the following animation commands will be applied to all open universes if the option key is held down when the command is selected.

Animate Forward
When selected, this item runs the simulation in the front-most universe forward in time.

Animate Backward
When selected, this item runs the simulation in the front-most universe backward in time.

Stop Animation
When selected, this item stops the simulation in the front-most universe.

Step Forward
When selected, this item runs the simulation in the front-most universe forward one time step.

Step Backward
When selected, this item runs the simulation in the front-most universe backward one time step.

Update Initial State
When selected, this item updates the initial state of the front-most universe so that it includes the current positions and velocities of all bodies in the universe.

Reset
When selected, this item stops the simulation in the front-most universe and returns the universe to its initial state (the state the universe was in when a body was last created, edited or deleted).

Window Menu

The Window menu contains the following items and is used to close windows, show and hide the clipboard and toolbars and to select document windows.

Close Window
When selected, this item closes the front-most window.

On Mac OS, if the option key is held down while selecting this item, all windows will be closed.

Show/Hide Clipboard
When selected, this item toggles the Clipboard window.

Toolbars
This item leads to a hierarchical menu that is used to show and hide various toolbars. Available toolbars include: File and Edit, Universe, Layout, Navigation and Animation.

Universe Window(s) (dynamic)
When selected, this item brings the named universe to the front. As universe windows are opened and closed, they are added and removed to and from this menu. The window list is kept in alphabetical order.

Help Menu

On Mac OS, the Help menu contains the following items and is used to access different types of on-line help.

About Balloon Help...
When selected, this item provides information about Balloon Help.

Show/Hide Balloons
When selected, this item toggles Balloon Help on/off. When Balloon Help is on, short help messages appear next to the cursor as it moves over various user interface elements. In Newton's Aquarium, help balloons are provided for all menu, dialog and toolbar items.

User's Guide When selected, this item opens the User's Guide (this file) using the default web browser on the system. An internet connection is not required to view the User's Guide.

Windows and Dialogs

Universe Window

The Universe window is where bodies are created and edited and where the results of the simulation are graphically displayed.

The status bar at the bottom of the window contains the following information:

Camera View
This is both a display and an input button that leads to a list of options. Possible settings include XY-Plane, XZ-Plane and YZ-Plane. Each option offers a different coordinate view of the universe.

Number of Bodies
This indicates the number of bodies in the universe at all times. If a simulation is running, the body count will decrease as collisions occur.

Elapsed Time
This indicates how long a simulation has been running for in days (d), hours (h), minutes (m) and seconds (s).

Open Dialog

The Open dialog box is used to retrieve universe documents from disk. For the most part, the Open dialog in Newton's Aquarium looks and works as it does in most Macintosh applications.

In addition to opening native universe documents, the dialog can also be used to "import" documents created by other gravity simulators. The Show popup menu at the bottom of the dialog is used to indicate what document format to read.

Save Dialog

The Save dialog box is used to store universe documents on disk. For the most part, the Save dialog in Newton's Aquarium looks and works as it does in most Macintosh applications.

A universe document can be stored in the usual manner or as stationery pad. A stationery pad is a template that describes the document. When a stationery pad is opened, a copy of the document is read into a new, untitled, window, leaving the original file untouched. Use the icons at the bottom right of the dialog to indicate whether a normal document, or a stationery pad, is being saved.

Edit Universe Dialog

The Edit Universe dialog is used to edit various attributes of a universe. The dialog contains the Physics, Appearance and Comments panels, which group together related universe attributes. The Appearance panel is further divided into Universe and Bodies sub-panels. Use the "tabs" near the top of dialog to select a panel to view and edit.

Physics Panel

Appearance Panel, Universe Sub-Panel

Appearance Panel, Bodies Sub-Panel

Comments Panel

Edit Body Dialog

The Edit Body dialog is used to edit various attributes of a body. The dialog contains the Physics and Appearance panels, which group together related body attributes. Use the "tabs" near the top of the dialog to select a particular panel to view and edit.

Physics Panel

Appearance Panel

Clipboard Window

The clipboard is a place where various types of information can be temporarily stored for later use. Objects such as text, graphics and universe bodies are moved to and from the clipboard using the Cut, Copy and Paste commands. Also see Edit menu and File & Edit toolbar.

The Clipboard window is used to display what is currently on the clipboard and is shown and hidden using the Show/Hide Clipboard item in the Window menu.

Appendix

Keyboard Shortcuts

Keyboard shortcuts allow frequently used functions to be quickly and easily accessed from the keyboard and often involve one or more modifier keys. Most keyboard shortcuts correspond to menu items and are part of the menu display. In addition, there are also a number of "hidden" shortcuts that are not explicitly documented in the program.

Menus
Holding down the option key causes certain menu items to "apply to all objects", where an object is one or more bodies, windows, documents, etc.

For example, Animate Forward becomes Animate All Forward when the option key is held down and will start the simulation in all open universes instead of just the front-most universe. Being able to start more than one universe at the exact same moment is useful for making comparisons between systems.

To discover which menu items can "apply to all objects", hold down the option key while exploring the menus. The names of various menu items will change to include the word "All".

Toolbars
Since most toolbar tools are simply button shortcuts for menu items, the option key works the same way with toolbar tools as it does with menu items.

Universe Windows
There are several keyboard shortcuts that apply to universe windows.

When no bodies are selected, the cursor keys translate the universe view. When the control key is also held down, the universe view is translated by a smaller amount. When one or more bodies are selected, the cursor keys translate the bodies instead.

In addition to moving bodies, the keyboard can be used together with the mouse to perform several common tasks. Clicking a body with the shift key held down allows multiple bodies to be selected and deselected. Pressing return opens the Edit Body dialog box for each selected body. Dragging a body with the option key held down makes a copy of the body. Dragging a body with the command key held down snaps the body to the nearest grid point if Snap to Grid is off (or allows a body to be freely positioned if Snap to Grid is on).

Pressing the escape key stops the simulation in the front-most universe. Pressing the escape key while holding down the option key stops the simulation in all universes.

Holding down the command key while clicking a document's window title will display a popup menu that indicates where the file resides.

Glossary

A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z

acceleration

The rate of change of velocity with respect to time.

accretion

The colliding and sticking together of small particles to make larger masses.

angular momentum

The tendency for bodies, because of their inertia, to keep spinning or orbiting.

aphelion

For a body orbiting the Sun, the point on its orbit that is farthest from the Sun.

apogee

The point in its orbit where an Earth satellite is farthest from the Earth.

asteroid

(Minor planet) one of several thousand very small members of the solar system that revolve around the Sun, generally between the orbits of Mars and Jupiter.

asteroid belt

The region lying between the orbits of Mars and Jupiter, containing the majority of asteroids.

axis

One of two or more reference lines in a coordinate system; also, the straight line, through the poles, about which a body rotates.

binary stars

Two stars bound together by gravity that revolve around a common centre of mass.

black hole

A mass that has collapsed to such a degree that the escape velocity from its surface is greater than the speed of light, so that light is trapped by the intense gravitational field.

centre of mass

The balance point of a set of interacting or connected bodies.

centripetal acceleration

The acceleration of a body toward the centre of a circular path.

centripetal force

A force required to divert a body from a straight path into a curved one, directed toward the centre of the curve.

circular velocity

The speed at which an object must travel to maintain uniform circular motion around a gravitating body.

comets

Bodies of small mass that revolve around the Sun, usually in highly elliptical orbits, and consist, in the dirty-snowball model, of small, solid particles of rocky material imbedded in frozen gases.

conservation of energy

A fundamental principle in physics that states that the total energy of an isolated system remains constant regardless of whatever internal changes may occur.

conservation of momentum

The physical principle stating that, with no outside net forces, the total momentum of an isolated system is constant.

coplanar

Lying in the same plane.

cosmology

The study of the nature and evolution of the physical universe.

cosmos

The Universe considered as an orderly and harmonious system.

eccentricity

The ratio of the distance of a focus from the centre of an ellipse to its semimajor axes.

ellipse

A plane curve drawn so that the sum of the distances from a point on the curve to two fixed points is constant.

energy

The ability to do work.

ephemeris

(pl., ephemerides) A table that gives the positions of celestial objects at various times.

equilibrium

A state of a physical system in which there is no overall change.

escape velocity

The speed a body must achieve to break away from the gravity of another body and never return to it.

force

A physical unit that describes the "push" needed to cause mass to accelerate.

forced motion

Any motion under the action of a net force.

frame of reference

A set of axes with respect to which the position or motion of something can be described or physical laws can be formulated.

galaxy

A huge assembly of stars (between 10^6 and 10^2), plus gas and dust, that is held together by gravity; the Galaxy, our own galaxy, containing our Sun.

general theory of relativity

The idea developed by Albert Einstein that mass and energy determine the geometry of spacetime and that any curvature of this spacetime shows itself by what we commonly call gravitational forces; Einstein's theory of gravity.

geocentric

Centred on the Earth.

gravitation

In Newtonian terms, a force between masses that is characterized by their acceleration toward each other; the size of the force depends directly on the product of the masses and inversely on the square of the distance between them; in Einstein's terms, the curvature of spacetime.

gravitational field

The property of space having the potential for producing gravitational force on objects within it; characterized by the acceleration of free masses.

gravitational force

The weakest of the four forces of nature; all particles with nonzero mass attract to each other.

gravitational mass

The mass of an object as determined by the gravitational force it exerts on another object.

gravitational potential energy

Potential energy related to a body's position in a gravitational field.

Halley's Comet

The periodic comet (orbital period about 76 years) whose orbit was first worked out by Edmund Halley from Newton's laws; has a small nucleus (about 10 km diameter), dark, irregular in shape and emitting jets of gas and dust.

heliocentric

Centred on the Sun.

hertz

A physical unit of frequency equal to 1 cycle/s.

hyperbola

A curve produced by the intersection of a plane with a cone; the shape of the orbit of a body with more than escape velocity.

inertia

The resistance of an object to a force acting on it because of its mass.

joule

A physical unit of work and energy.

jovian planets

Planets with physical characteristics similar to Jupiter: large mass and radius, low density, mostly liquid interior.

Kepler's laws

Kepler's three laws of planetary motion that describe the properties of elliptical orbits with an inverse-square force law.

kinetic energy

The ability to do work because of motion.

mass

A measure of an object's resistance to change in its motion (inertial mass); a measure of the strength of a gravitation force an object can product (gravitational mass).

meteorite

A solid body from space that survives a passage through the Earth's atmosphere and falls to the ground.

momentum

The product of an object's mass and velocity.

newton

The SI unit of force, named after the English mathematician and physicist Sir Isaac Newton (1642-1727).

orbit

The path of an object that is moving around a second object or point.

parabola

A geometric figure that describes the shape of an escape-velocity orbit.

perigee

The point in its orbit at which an Earth satellite is closest to the Earth.

period

The time interval for some regular event to take place; for example, the time required for one complete revolution of a body around another.

physical universe

The parts of the Universe that can be seen directly plus those that can be inferred from the laws of physics.

planet

From the Greek word for "wanderer"; any of the nine (so far known) large bodies that revolve around the Sun; traditionally, any heavenly object that moved with respect to the stars (in this sense, the Sun and the Moon were also considered planets).

position

A location relative to some other location.

potential energy

The ability to do work because of position; it is storable and can later be converted into other forms of energy.

reference frame

A set of coordinates by which position and motion may be specified.

relativity

Two theories proposed by Albert Einstein; the special theory describes the motion of nonaccelerated objects, and general relativity is a theory of gravitation.

retrograde motion

The apparent anomalous westward motion of a planet with respect to the stars, which occurs near the time of opposition (for an outer planet) or inferior conjunction (for an inner planet).

revolution

The motion of a body in orbit around another body or a common centre of mass.

solar system

A collection of planets and moons orbiting a star. A solar system may also contain other smaller objects, such as asteroids.

space

A three-dimensional region in which objects move and events occur and have relative direction and position.

speed

The rate of change of position with respect to time and not indicating direction; see velocity.

star

A brightly burning large volume of matter.

time

A measure of the flow of events.

universal law of gravitation

Newton's law of gravitation; see gravitation.

universality of physical laws

The assumption, borne out by some evidence, that the physical laws understood locally apply throughout the Universe and perhaps tot he Universe as a whole.

Universe

The totality of all space and time; all that has been, is and will be.

vector

The distance between two points as well as the direction from one point relative to the other.

velocity

The rate of change of position with respect to time; see speed.

weight

The total force on some mass produced by gravity.

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