The Solar System - orbits of the planets around the Sun and the Moon around the Earth - the four seasons - autumn and vernal equinox - summer and winter soltice - ocean tides and moon phases

Satellite playground
This simulation shows the orbits of three satellites around the Earth (how to edit orbits):

- a geostationary satellite has a circular orbit in the plane of the Earth's equator. It is just the right distance from the Earth that it orbits at the same angular speed that the Earth rotates - so it stays above exactly the same spot on the equator;

- a satellite with a very low and fast circular orbit that takes it over the Earth's pole. As the Earth rotates, the satellite flies over a different part of the Earth on each orbit. Spy satellites might use such an orbit;

- a satellite with an elliptical orbit in the plane of the Earth's equator.

The simulation gives two simultaneous views of the Earth and satellites; a 3D view (from an adjustable point in space - or from any of the satellites) and a selection of plane views (top, front or side).

The plane views show the velocity (blue arrows) and acceleration (green arrows) of the satellites. The acceleration of the satellites is always towards the centre of the Earth. The acceleration and velocity of a satellite is higher the closer it is to the Earth.

To change the orbit of any satellite, pause the simulation, then use the mouse on any the the plane views (top, front or side) to move the satellite or alter its velocity. (Try to avoid moving the Earth by mistake.)

Experiment changing the trajectory of one of the satellites - then watch what happens. You'll get an especially good view from the satellite itself!
Once you've changed a satellite's orbit, the label it started out with may longer be true, and it might even hit the Earth or escape its gravitational pull altogether.
Whatever happens, clicking the "rewind" button will return the simulation to its original state.

The energy and orbital period of the satellite in the elliptical orbit is shown in a scrolling graph. While the satellite moves closer to the Earth its gravitational potential energy is converted into kinetic energy. As it moves away from the Earth the kinetic energy is converted back to gravitational potential energy. All the while the total KE+PE remains constant.

As long as the satellite's total energy is less than zero, it will remain in a closed orbit around the Earth [providing it doesn't crash into it, or get diverted by another object in the Solar System].
If you adjust the satellite's position and/or velocity so that its total energy is greater than zero - then it will completely escape the Earth's gravitational pull.

Two factors (not taken into account in this simulation) diminish the long term stability of a satellite's orbit;

- at low orbits, the air friction of the thin remnants of the atmosphere will slow satellites down so that they spiral lower and lower - eventually burning up in the atmosphere or crashing into the Earth;

- the pull of the Earth's equatorial bulge, the Sun and the Moon, will cause the axis of a satellite's orbit to precece like a top [as does the Earth's axis (once every 26 000 years) and the axis of the Moon's orbit (once every 18.6 years) ]

Note:
Watching the view from the polar satellite, you'll notice the view switch around each time the satellite passes over either pole. This happens because the camera adjusts to try to keep the North pole uppermost in the picture.

Notice that the satellite's gravitational potential energy is always registered as negative - below the horizontal "zero" line on the graph. This is because, by convention, we say that the gravitational potential energy between two objects is zero when they are an infinite distance apart. Since this is also their maximum potential energy, the potential energy for objects a finite distance apart is less than zero.
This may seem confusing, but it is actually the simplest way of defining gravitational potential energy. Otherwise we'd have to specify some arbitrary separation for zero PE, and we'd have to deal with both positive and negative PE

-	a geostationary satellite has a circular orbit in the plane of the Earth's equator. It is just the right distance from the Earth that it orbits at the same angular speed that the Earth rotates - so it stays above exactly the same spot on the equator;
-	a satellite with a very low and fast circular orbit that takes it over the Earth's pole. As the Earth rotates, the satellite flies over a different part of the Earth on each orbit. Spy satellites might use such an orbit;
-	a satellite with an elliptical orbit in the plane of the Earth's equator.

-	at low orbits, the air friction of the thin remnants of the atmosphere will slow satellites down so that they spiral lower and lower - eventually burning up in the atmosphere or crashing into the Earth;
-	the pull of the Earth's equatorial bulge, the Sun and the Moon, will cause the axis of a satellite's orbit to precece like a top [as does the Earth's axis (once every 26 000 years) and the axis of the Moon's orbit (once every 18.6 years) ]