Open Access. Powered by Scholars. Published by Universities.®

Physics Commons

Open Access. Powered by Scholars. Published by Universities.®

Articles 1 - 10 of 10

Full-Text Articles in Physics

General Relativity, 4, David Peak Jan 2018

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 Jan 2018

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 107 to 1011 stars bound together by gravity. In the currently observable universe, it is estimated that there are roughly 1011 galaxies. The dilute fog is 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 2H (deuterium), 3He , and 7Li . The ratio of ...


General Relativity, 2, David Peak Jan 2018

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 m1 is at x1(t) and m2 is at x2(t). Newton’s gravitational force law says F1on 2(t) = Gm1m2 / [x2(t) − x1(t)]2 and relativistic dynamics says dp2 /dt = F1on 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 x1(t) and x2(t) are the simultaneous ...


General Relativity, 9, David Peak Jan 2018

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 Jan 2018

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 Jan 2018

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 Jan 2018

Inflation (Excel), David Peak

General Relativity

No abstract provided.


General Relativity, 7, David Peak Jan 2018

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 Jan 2018

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 Jan 2018

General Relativity, 5, David Peak

General Relativity

No abstract provided.