This activity taken from Society of Physics Students outreach manual: https://www.spsnational.org/sites/default/files/files/programs/2012/soc…
Tell students they will be using the gravity well to model the shapes and speeds of orbiting objects. They release their marble so that it orbits the centre well of the fabric. The centre well models the gravity of the sun/a star/a black hole (depending on the emphasis of the lesson). Their marble may model a planet, dwarf planet, asteroid, comet orbiting a star. Or their marble can model a star orbiting a black hole.
(See below for comments on how this model is different from real astronomical objects in orbit.)
As students experiment, prompt them to notice the shapes of the orbits they make, and maybe also the speed of the marble at different distances from the well.
Discussion on orbit shapes
Ask students what shaped orbits they made, and compare their descriptions to orbit shapes of astronomical objects. Our familiar planets have a circular orbit, whereas comets and several trans-Neptunian dwarf planets have elliptical orbits.
Show images of various orbits (of planets, moons, dwarf planets, asteroids, Kuiper belt objects and comets), during experimentation or after.
Try this image for comet orbits: http://www.wired.com/images_blogs/wiredscience/2013/08/Orbits_of_period…
Try this page for images for orbits of dwarf planets in the solar system, to give a sense of how many objects orbit the sun: http://www.duncansteel.com/archives/2140 or do an image search of "orbit Eris Haumea Makemake").
Discussion on why objects orbit: they are continually "falling" towards the sun, or central gravity well, but as they are in forward motion, they never reach it, but instead curve around it.
Note on why our planets' have a circular orbit: maybe because they were formed from a spinning disc of debris, so all end up in the same plane. Also, if they were not circular, we would not be here to observe them! (Our distance from the sun would change a lot, making a challenge for life to survive.)
Kindergarteners and young primaries can draw the shapes they made with their marble: circle, elipse, long narrow elipse, star shape as the ellipses cycle round. Orbits in the galaxy are all these shapes.
Several marbles orbiting at once can represent the asteroid belt, with collisions that knock some of them out of orbit.
Using the gravity well to model stars orbiting a black hole
Stars orbit black holes, so astronomers look for stars that appear to be orbiting around "nothing", as evidence for the presence of a black hole. By mapping the locations of all objects in orbit, the location and size of the black hole can be calculated.
Show students an image of star orbits around a black hole. Try this image, or search images for "SgrA* orbits": https://inspirehep.net/record/800608/files/f16.png
To modify the gravity well model to be more like the shape of the gravity well of a black hole, add a ring underneath to model the event horizon (the point past which nothing can escape from a black hole's gravity). See the last two photos.
Discussion about orbit speeds
Ask students to notice what happens to the speed of an orbit as the object approaches the gravity well of the sun, as astronomical objects behave the same. They speed up near the object they are orbiting, gaining kinetic energy. As they move outwards they lose speed, but gain another kind of energy - gravitational potential energy. (Similar to a ball been thrown in the air or a roller coaster ride.) Planets with large orbits spend most of their time far from the sun, where they are moving more slowly.
A black hole has an event horizon, past which the object cannot escape its gravity, however much energy it has.
Using the gravity well to model how the moon causes tides
Information on classes of objects that orbit the sun
Planets - now 8 planets, as Pluto is now classified as a dwarf planet. To be a planet, an object needs to 1. be massive enough to pull itself into a sphere under its own gravity 2. is not massive enough to cause thermonuclear fusion (like a star) and 3. has cleared its neighbouring region of smaller objects i.e. they are attracted by its gravity.
Dwarf planets - large enough to be spherical, but too small to clear their neighbourhood of smaller objects. There are many many dwarf planets orbiting the sun, and more are continuously being discovered. Examples: Ceres in the asteroid belt, Trans Neptunian objects (TNOs) such as Pluto, Eris, Makemake, Haumea.
Asteroids - small irregularly shaped objects made of rock, metal or a mixture of both, found in the asteroid belt. Image of main asteroid belt at: http://www.rawscience.tv/wp-content/uploads/2014/09/asteroid-belt.jpg
Comets - snowballs of frozen gases, rock and dust the size of a small town. A comet warms up near the sun and develops a coma (atmosphere), a glowing head, hundreds of thousands of km across. It has two tails (which always point away from sun), one gas and one dust (which curves with sun’s gravity). Image of comet structure through its orbit: http://www.skyandtelescope.com/wp-content/uploads/Koehn_IZ_orbit_300dpi… Comets may have brought water and organic compounds (the building blocks of life) to Earth and other bodies in our solar system. There are billions of them. Image of some comet orbits at: http://www.wired.com/images_blogs/wiredscience/2013/08/Orbits_of_period… (Orbit times: Halley orbit is 76 years, Borrelly orbit is 7 years, Ikeya–Zhang orbit is 366 years and is the longest known orbital period.)
Differences between this gravity well and real orbiting objects
Ask older students for ideas in how their model is different from real orbiting objects at the end of this activity.
In this model, every marble inevitably loses energy to friction as it rubs against the cloth and falls into the gravity well. In the vacuum of space there is no friction, and orbit shapes are maintained, as long as there are no collisions.
Physicists use this kinds of model of gravity, though they would use mathematics to describe the shape of a gravity well, rather than a physical object. The more massive the body, the deeper and more extensive the gravity well associated with it. Black hole has a very deep well.