# APPEAL 2013

Universal Gravitation: A History of Surprises

steven.balbus@astro.ox.ac.uk

The language of gravity

The above left slide shows 1 = Newton (connected with mass), 2 = Einstein (space-time curves) and 3 = Feynman (focuses on electricity/magnetism and radiation is a fundamental property). The above right slide has the geometrical term with entries for pressure/momentum. R means the curvature. Richard Feynman used the quantum mechanics approach.

The formula on the above right slide is a vector form of the formula that A level students meet.

http://en.wikipedia.org/wiki/Isaac_Newton

http://en.wikipedia.org/wiki/Newton’s_law_of_universal_gravitation

Every point mass attracts every single other point mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them.

Gauss formulated a simpler version (see the above picture on the left).

http://en.wikipedia.org/wiki/Carl_Friedrich_Gauss

http://en.wikipedia.org/wiki/Divergence_theorem

http://en.wikipedia.org/wiki/Gauss%27_law_for_gravity

http://en.wikipedia.org/wiki/Poisson’s_equation

The r is the above right slide is the radius on the sphere.

The universe has to be dynamic.

Gravity on large scales

In the slides below r is a distance.

In the above left slide r is a distance, R is a scale factor, E is an energy-like term, G is the universal gravitational constant and r is energy density.

There must be a reversal for the structure to form in an accelerating universe.

COBE shows the fluctuation in the density field.

http://en.wikipedia.org/wiki/Cosmic_Background_Explorer

The Cosmic Background Explorer (COBE), also referred to as Explorer 66, was a satellite dedicated to cosmology. Its goals were to investigate the cosmic microwave background radiation (CMB) of the universe and provide measurements that would help shape our understanding of the cosmos. This work provided evidence that supported the Big Bang theory of the universe: that the CMB was a near-perfect black-body spectrum and that it had very faint anisotropies. Two of COBE’s principal investigators, George Smoot and John Mather, received the Nobel Prize in Physics in 2006 for their work on the project. According to the Nobel Prize committee, “the COBE-project can also be regarded as the starting point for cosmology as a precision science”.

The Grecco simulation follows 134217728 dark matter particles in a comovin box of size 150 Mpc/h from z = 20 to z = 0. This simulation has cosmological parameters according to WMAP5 and was runnned in Geryon cluster @ Astronomy and Astrophysics Department, Pontificia Universidad Católica, Chile.

The universe has dark voids. Parts of the universe expanded more than others producing an asymmetrical foam structure. The simulation shows a crude structure only.

Gravitational timescales

Gravitational equilibrium

When a star is on the main sequence it maintains its shape because there is an outward thermal pressure from the hot core, balanced by the inward gravitational pressure from the overlying layers.

http://en.wikipedia.org/wiki/Main_sequence

http://en.wikipedia.org/wiki/Hydrostatic_equilibrium

The slides below show some scary maths that describes the hydrostatic equilibrium.

Spherical case is special so we can ignore the outside. We can’t do this if the star is a cube.

http://en.wikipedia.org/wiki/Lord_Kelvin

http://en.wikipedia.org/wiki/Hermann_von_Helmholtz

https://en.wikipedia.org/wiki/Pressure

http://en.wikipedia.org/wiki/Kelvin%E2%80%93Helmholtz_mechanism

The Kelvin–Helmholtz mechanism is an astronomical process that occurs when the surface of a star or a planet cools. The cooling causes the pressure to drop and the star or planet shrinks as a result. This compression, in turn, heats up the core of the star/planet. This mechanism is evident on Jupiter and Saturn and on brown dwarfs whose central temperatures are not high enough to undergo nuclear fusion. It is estimated that Jupiter radiates more energy through this mechanism than it receives from the Sun, but Saturn might not.

The mechanism was originally proposed by Kelvin and Helmholtz in the late 19th century to explain the source of energy of the Sun. By the mid-19th century, conservation of energy had been accepted, and one consequence of this law of physics is that the Sun must have some energy source to continue to shine. Because nuclear reactions were unknown, the main candidate for the source of solar energy was gravitational contraction. However, it soon was recognized by Sir Arthur Eddington and others that the total amount of energy available via this mechanism only allowed for the Sun to shine for millions of years rather than the billions of years that the geological and biological evidence suggested for the age of the Earth. (Kelvin himself had argued that the earth was millions, not billions, of years old.) The true source of the Sun’s energy remained uncertain until the 1930s in which it was shown by Hans Bethe to be nuclear fusion

http://en.wikipedia.org/wiki/Virial_theorem

In mechanics, the virial theorem provides a general equation that relates the average over time of the total kinetic energy, , of a stable system consisting of N particles, bound by potential forces, with that of the total potential energy, , where angle brackets represent the average over time of the enclosed quantity.

The above slide on the right is showing that gravitational potential energy is related to thermal energy.

The contraction occurs off the main sequence.

Gravitational tidal forces

http://en.wikipedia.org/wiki/Tidal_force

The tidal force is a secondary effect of the force of gravity. It arises because the gravitational force exerted by one body on another is not constant across its diameter. The nearest side is attracted more strongly than the farthest side. Thus, the tidal force is differential. In a more general usage in celestial mechanics, the expression ‘tidal force’ can refer to a situation in which a body or material is mainly under the gravitational influence of a second body, but is also perturbed by the gravitational effects of a third body. The perturbing force is sometimes in such cases called a tidal force (for example, the perturbing force on the Moon): it is the difference between the force exerted by the third body on the second and the force exerted by the third body on the first.

l = latitude and i = inclination

Earth is losing energy as it rotates and this energy is transferred to the Moon which is why it the Moon is moving away.

Take the Cambrian explosion solar contribution of 36% at face value

http://en.wikipedia.org/wiki/Black_hole_thermodynamics

http://www.sukidog.com/jpierre/strings/bholes.htm

http://en.wikipedia.org/wiki/Cumrun_Vafa

http://en.wikipedia.org/wiki/Andrew_Strominger

Andrew Strominger wrote a paper with Cumrun Vafa that explains the microscopic origin of the black hole entropy, originally calculated thermodynamically by Stephen Hawking and Jacob Bekenstein, from string theory.