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## Full-Text Articles in Physics

General Relativity, 4, David Peak

#### General Relativity, 4, David Peak

*General Relativity*

*Orbital motion of small test masses *

The starting point for analyzing free fall trajectories in the (2-space, 1-time) Schwarzschild spacetime is Equation (3) from GR 3:

General Relativity, 6, David Peak

#### General Relativity, 6, David Peak

*General Relativity*

*Modern cosmography *

The “normal” matter in the universe—i.e., stuff made of protons, neutrons, and electrons— consists, approximately, of lumps floating in a dilute fog. The lumps are galaxies, clusters of 10^{7} to **10 ^{11} stars** bound together by gravity. In the currently observable universe, it is estimated that there are roughly

**10**. The dilute fog is

^{11}galaxies**primarily neutral atomic hydrogen gas with some helium-4 mixed**in (making up a total of 98% or more of the fog); there are also very small fractions of

^{2}H (deuterium),

^{3}He , and

^{7}Li . The ratio of ...

General Relativity, 2, David Peak

#### General Relativity, 2, David Peak

*General Relativity*

Newton’s law of gravitostatics is incompatible with special relativity. To see this, suppose at time t in frame O m_{1} is at x_{1}(t) and m_{2} is at x_{2}(t). Newton’s gravitational force law says F_{1on 2}(t) = Gm_{1}m_{2} / [x_{2}(t) − x_{1}(t)]^{2} and relativistic dynamics says dp_{2} /dt = F_{1on 2}. Transforming to another frame Oʹ moving relative to O leads to dp′_{2}/dt′ = F′_{1on 2}. But what is F′_{1on 2} ? If x_{1}(t) and x_{2}(t) are the simultaneous ...

General Relativity, 9, David Peak

#### General Relativity, 9, David Peak

*General Relativity*

*Cosmic development *

As discussed in GR 8, the cosmic scale factor a in the FLWR s-t obeys the Friedmann equation

General Relativity, 3, David Peak

#### General Relativity, 3, David Peak

*General Relativity*

Gravity as geometry: part II

Even in a region of space-time that is so small that tidal effects cannot be detected, gravity still seems to produce curvature. The argument for this point of view starts with the recognition that, for mechanical systems, it is impossible to distinguish a frame of reference with a uniform gravitational field from a uniformly accelerating frame that has no gravity. Thus, for example, in a (small) rocket ship with no windows it is not possible to determine whether the weight one reads standing on a scale at the tail of the rocket is due to ...

General Relativity, 8, David Peak

#### General Relativity, 8, David Peak

*General Relativity*

*The Cosmic Microwave Background (CMB)*

As previously noted, the universe is filled with microwave radiation. The frequency spectrum of this ubiquitous radiation follows a blackbody curve, as shown to the right. (http://map.gsfc.nasa.gov/media/ContentMedia/990015b.jpg) Note that photon energy (proportional to 1/wavelength) increases to the right. You might think the curve shown is the plot of a theoretical equation, but what is shown is actual measured data taken during the flight of the COBE (Cosmic Microwave Explorer) satellite/microwave observatory in 1990. The uncertainties in the measurements are about the thickness of the curve ...

Inflation (Excel), David Peak

General Relativity, 7, David Peak

#### General Relativity, 7, David Peak

*General Relativity*

*The expanding universe *

The fact that the vast majority of galaxies have a spectral redshift can be interpreted as implying that the universe is expanding. This interpretation stems from the Doppler effect in which the relative motion of an emitter and a detector produces a frequency shift of the detected light with respect to the emitted light.

General Relativity, 1, David Peak

#### General Relativity, 1, David Peak

*General Relativity*

In special relativity, events occur in the arena of space-time which may be coordinatized differently by different observers, but which is otherwise immutable. Adding gravity to relativity provides an amazing result: space-time becomes “organic,” taking its form from the matter and energy it contains. This is Einstein’s general theory of relativity and it has the capacity to tell us about the past and future of the universe. Embedded in the history book of the cosmos are several chapters on the origins of matter. As a result, relativity + gravity unites the structures of matter on the largest and smallest scales.

General Relativity, 5, David Peak