Create a simple apparatus to demonstrate a gravity well.
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Teachable Topics:
- gravity
- orbital mechanics
- Kepler's Laws
Theory:
A gravity well represents the gravitational field of an object. Massive objects (such as stars and planets) bend spacetime, causing space to curve around the object.
The more massive the object, the deeper the well. For example, the Earth is much more massive than the Moon and so has a deeper gravity well or a stronger gravitational field.
The deeper the gravity well, the more energy is required to escape from it. This is why the Earth has a much higher escape velocity than the Moon.
The well represents the gravitational potential field that surrounds an object. The orbit of a body around another (a planet around a star, for example) is determined by this field. You can craft your own gravitational well to help study the orbital mechanics of celestial bodies. For example, when you toss a ball into this well, you will notice that it travels faster when it is closer to the centre. This is a demonstration of Kepler's Second Law, which states that a line joining the Sun and a planet sweeps out equal areas in an equal amount of time.
The orbits of the planets around the Sun are elliptical, and so a planet’s distance from the Sun changes over the course of an orbit. As such, the velocity of the planet also varies over an orbit. When the planet is close to the Sun it must sweep out a longer path in the same amount of time, so it must travel with greater velocity. The planet travels faster when it is closer to the Sun and slower when it is further away. This is a result of conservation of angular momentum.
Apparatus:
- stretchy fabric (we used 1.5 x 1.5 m of nylon/spandex)
- metal beams to make a frame (we made a 1.25 x 1.25 m steel frame)
- strong magnets to secure fabric to beams
- 2 more strong magnets to create the well
- a mass to create the well (the larger the mass, the larger the well)
- ball to throw into the well
Procedure:
- assemble a square metal frame
- secure fabric to frame using strong magnets
- to create the well:
- in the middle of the frame, place one magnet on top of the well
- attach the other magnet to the bottom of the well
- attach a mass to the magnet on the bottom of the well
- throw a ball into the well to demonstrate bodies orbiting around a gravity well
