## Astronomy: A Physical PerspectiveThis fully revised and updated text is a comprehensive introduction to astronomical objects and phenomena. By applying some basic physical principles to a variety of situations, students will learn how to relate everyday physics to the astronomical world. The text contains useful equations, chapter summaries, worked examples and end-of-chapter problem sets. It is suitable for undergraduate students taking a first course in astronomy, and assumes a basic knowledge of physics with calculus. |

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Spaghettification

From Wikipedia, the free encyclopedia

For the computer programming term, see spaghetti code.Tidal forces acting on a spherical body in a non-homogeneous gravitational field. The effect originates from a source to the right (or to the left) of the diagram. Longer arrows indicate stronger forces.

In astrophysics, spaghettification (sometimes referred to as the noodle effect[1]) is the vertical stretching and horizontal compression of objects into long thin shapes (rather like spaghetti) in a very strong non-homogeneous gravitational field; it is caused by extreme tidal forces. In the most extreme cases, near black holes, the stretching is so powerful that no object can withstand it, no matter how strong its components. Within a small region the horizontal compression balances the vertical stretching so that small objects being spaghettified experience no net change in volume.

Stephen Hawking[2] describes the flight of a fictional astronaut who, passing within a black hole's event horizon, is "stretched like spaghetti" by the gravitational gradient (difference in strength) from head to toe. The reason this happens would be because the gravity exerted from the singularity would be much stronger at one end of your body from the other. If one were to fall into a black hole feet first, the gravity at his/her feet would be much stronger than at their head, causing the person to be vertically stretched. Along with that, the right side of the body will be pulled to the left, and the left side of the body will be pulled to the right, horizontally compressing the person.[3] However, the term "spaghettification" was established well before this.[4]

Contents [hide]

1 A simple example

2 Examples of weak and strong tidal forces

3 Inside or outside the event horizon

4 Notes

5 References

A simple example[edit]

The spaghettification of four objects falling towards a planet

Imagine four separate objects in the space above a planet, positioned in a diamond formation. The four objects follow the lines of the gravitoelectric field,[5] directed towards the celestial body's centre. In accordance with the inverse-square law, the lowest of the four objects experiences the biggest gravitational acceleration, so that the whole formation becomes stretched into a line.

Now imagine these four objects as connected parts of a larger object. A rigid body will resist distortion, and internal elastic forces develop as the body distorts to balance the tidal forces, so attaining mechanical equilibrium. If the tidal forces are too large, the body may yield and flow plastically before the tidal forces can be balanced, or fracture, producing either a filament or a vertical line of broken pieces.

Examples of weak and strong tidal forces[edit]

In the gravity field due to a point mass or spherical mass, for a uniform rod oriented in the direction of gravity, the tensile force at the center is found by integration of the tidal force from the center to one of the ends. This gives F =

μ l m

/

4r3

, where μ is the standard gravitational parameter of the massive body, l is the length of the rod, m is rod's mass, and r is the distance to the massive body. For non-uniform objects the tensile force is smaller if more mass is near the center, and up to twice as large if more mass is at the ends. In addition, there is a horizontal compression force toward the center.

For massive bodies with a surface, the tensile force is largest near the surface, and this maximum value is only dependent on the object and the average density of the massive body (as long as the object is small relative to the massive body). For example, for a rod with a mass of 1 kg and a length of 1 m, and a massive body with the average density of the Earth, this maximum tensile force due to the tidal force is only 0.4 μN.

Due to the high density, the tidal force near the surface of a white dwarf is much stronger, causing in the example a maximum tensile force of up to 0.24 N. Near a neutron star, the tidal

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