Astrophysical Principles - Gravitation

Moon Orbit Model

Mechanical model of Earth-Moon orbit around Sun.

What it shows:

A model to demonstrate the precession of the Moon's orbit relative to the ecliptic. It is useful for discussing the conditions necessary for the occurrence of an eclipse.

How it works:

A large aluminum disk represents the plane of the Moon's orbit about the Earth. The disk lies flush with the box surface it sits in; the plane of the box representing the Ecliptic. The Moon's own orbit is inclined at 5° to the ecliptic, and precesses with an 18 year period. You...

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Precession Globe

Globe pivoted so north pole can precess.

What it shows:

Due to the oblateness of the Earth, the gravitational force between the Earth and the Sun sets up a couple which causes the Earth's axis of rotation to precess. An adapted globe shows what is meant by precession.

How it works:

An old 8" (19cm) globe has been modified 1 to allow it to precess on its axis. A 23° cone is cut into the south pole, and a cone of metal supported by a metal equatorial ring has been inserted. This makes the globe bottom heavy (and...

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Spherical Blackboard

What it shows:

You can use a spherical blackboard for many things, including the teaching of geographical coordinates, as a model for a closed Universe, or simply as a mathematical shape.

In the non-Euclidean geometry of the sphere, a circle will have a circumference greater than 2πr and an area greater than πr2. A triangle’s angles will add to more than 180°, and two parallel lines, called Great Circles, will converge.

A Universe with a density parameter Ω greater than unity will have too much mass to overcome its own gravitational...

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Saddle Shape Universe

Curved space segment for open universe geometry.

What it shows:

Whether the Universe continues to expand forever or will collapse back in upon itself depends upon the amount of matter it contains. For a density parameter Ω less than unity the Universe will not have enough mass to collapse and will be in a state of perpetual expansion. In general relativity, the curvature of space is dependent upon the density of the Universe, and for Ω<1 the curvature is negative or hyperbolic. It can be represented two dimensionally (see Comments) by a saddle...

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Gravitational Field Surface

1m diameter rubber sheet acts as curved space for ball bearing masses.

What it shows:

In general relativity, gravity is replaced by a curved space geometry, where the curvature is determined by the presence and distribution of matter. Objects move in straight lines, or along geodesics, but because of the curvature of space, their paths will simulate the effect of gravitational attraction. This demo gives a two dimensional view of warped space.

How it works:

In this 2-D analog, a 1 meter diameter piece of dental dam forms a...

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Gravitational Lens

Laser and plastic lens with curvature to simulate bending of light by massive object.

What it shows:

Gravitational lensing is caused by the bending of light rays by the gravitational field of an intervening object. The effect is seen with the Sun, but is most spectacular when a whole galaxy acts as a lens to a cosmologically distant object, such as a quasar. Depending on the geometry of the alignment and the structure of the lensing galaxy, the image of the quasar is distorted into two or more distinct images, sweeping arcs or a complete ring. Here we model...

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Potential Well Orbiter

Orbital motion simulated by ball rolling on wooden potential well.

What it shows:

Motion in a central potential is demonstrated by a ball rolling on a circular 1/r curved surface.

How it works:

The 1/r potential well simulates the gravitational potential surrounding a point mass; a ball bearing moving in this potential follows a parabolic or elliptical orbit depending upon its initial trajectory and velocity. As it loses energy due to friction, the orbit decays and the ball spirals towards the centre of the well. You could...

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Foucault Pendulum

Plane of pendulum oscillation appears to change due to rotation of Earth.

What it shows:

Due to the rotation of the Earth, the plane of oscillation of a pendulum will rotate with respect to the surface beneath it. We expect a rotation of about 10˚/hr at our latitude of 42.˚

How it works:

Here the observer standing on the Earth resides in the reference frame, with the swinging pendulum oscillating in a rotating frame. From the pendulum's point of view, it keeps oscillating in the same plane, but the Earth spins below it. The deflection from its original plane...

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Cavendish Experiment

Calculation of gravitational constant, with accompanying apparatus model.

What it shows

The gravitational attraction between lead spheres. The data from the demonstration can also be used to calculate the universal gravitational constant G.

gravitational attraction
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Reversible (Kater's) Pendulum

A physical pendulum with two adjustable knife edges for an accurate determination of "g".

What It Shows

An important application of the pendulum is the determination of the value of the acceleration due to gravity. By adding a second knife-edge pivot and two adjustable masses to the physical pendulum described in the Physical Pendulum demo, the value of g can be determined to 0.2% precision.

How It Works

Using a simple pendulum, the value of g can be determined by...

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Newton's Apple

Apple electronically released from platform; fall time given by special circuit and digital display.

What it shows:

This is a free-fall-from-rest experiment in which an apple (or any other object of comparable size) is dropped from the lecture hall ceiling into a catching bucket on the floor. By measuring the (1) distance and (2) duration of the fall, an accurate (± 0.022%) determination of the acceleration due to gravity can be made:

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