© J R Stockton, ≥ 2010-03-01

Links within this site :-

**Merlyn Home Page**- Site Index, E-Mail, Copying- Astronomy / Astronautics 1
- Astronomy / Astronautics 2
- Astronomy / Astronautics 3
- Astronomy / Astronautics 4
**This Page**:-- Gravity 1 :-
- Gravity 2 :-
- Gravity 3 :-
- Low Orbit Time
- Falling - from Orbit, from a Beanstalk
- The Paths of Moons
- Binding Energy of a Sphere
- Pressure Within a Sphere

- Gravity 4 :-
- Gravity 5 :-
- The Stability of a Tertiary Orbit - Moon-Earth Binding, The Hill Radius
- Horseshoe Orbits
- Tides
- The Roche Limit
- Planetary Rings

- The Geometry of Ellipses

NONE of the values given in these pages should be taken as exact, unless specifically so claimed. They have been obtained from various sources, including memory, and are for purposes of illustration ONLY, except sometimes.

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The site deals with the consequences of Newton's work; it disregards relativity, string theory, etc.

There is a ZIPped snapshot including these and other pages related to Astro and Gravity etc. (172kB+), taken on or after 2010-02-18; unZIP it in an empty directory.

There is no guarantee that these are the latest or best values. See Wikipedia, etc.

G × M_{Sun} = 1.32712440018×10^{20}
N m^{2} kg^{-1} (HS 20031230 news:s.p.p)

G = (6.674215±0.000092)×10^{-11}
m^{3}/kg/s^{2} ( Jens
H. Gundlach and Stephen M. Merkowitz);

Earth's mass : (5.972245±0.000082)×10^{24} kg

& Sun's mass : (1.988435±0.000027)×10^{30}
kg (G
& M)

Hubble constant : 70.4 ± 1.4 km/s / Mpc (68%) (WMAP, 2010)

Age of Universe : 13.75 ± 0.11 × 10^{9}
years (68%) (WMAP, 2010)

Planck density, 5.1×10^{96} kg/m^{3}

Age of Solar System : 4.5685 × 10^{9} years

Average radii : Earth : mean 6371 km, equatorial 6378 km, polar 6357 km; Moon 1739 km

Earth circumferences : polar 40007.863 km, equatorial 40075.017 km (WGS84 / Kaese))

Geosynchronous orbit radius : 42.164 Mm (authority?) ( → ~ 36 Mm high)

Standard Earth gravity : 9.80665 m s^{-2} (CGPM 3, 1901)

Standard atmospheric pressure at sea level : 101.325 kPa (CGPM 10, 1954)

Angles from Earth Orbit : Equator 23.4° ; Moon Orbit 5.2°

Eccentricity of Earth's orbit : currently 0.0167

Power of Sun : 3.86×10^{26} watts

Solar Constant : ~ 1361 W/m^{2}.

Solar wind dynamic pressure averages ~ 2 nPa at Earth; solar radiation ~10 µPa

Measurements and Units - see in Kaye & Laby Online.

Gravitational binding energy : U = 3GM^{2}/5r

Moment of Inertia : I = 2Mr^{2}/5

Now in The Geometry of Ellipses.

This section mentions advanced subjects that I recall comparatively little of.

There are relativity FAQs.

A part of my Astronomy / Astronautics 3 calculates relativistic travel.

Note - this is really not my subject - needs checking. Was there not a third confirmation of Einstein?

Presumed to be that of light. Newtonian gravity is instantaneous; making the speed finite introduces unwanted differences; proper relativity removes those.

The advance of the perihelion of Mercury is largely explained by Newtonian gravity. But there is a residual advance of 43" of arc per century, explained by Einstein's relativitistic gravitation.

Light passing near a massive body is deviated by gravity. Eddington's 1919 trip confirmed Einstein's relativitistic prediction of 1.74" of arc for Sun-grazing rays, twice the Newtonian value.

In that fashion, the Sun "focuses" light from infinity at a distance of 550 AU (the angular radius of the Sun as seen from there is 1.74"). Galaxies can focus more distant ones. Focusing is not lens-like, but it can magnify and intensify.

Light reaching a massive body is gravitationally blue-shifted, and
*vice versa*. This is not the Hubble-related shift; it can be shown
locally by using the Mössbauer effect.

Even classically, light cannot escape from a body which is
sufficiently large and concentrated, as judged by
*2GM/rc ^{2}*; but General Relativity is needed to attempt a
full explanation of Black Holes.

One can enter a sufficiently large Black Hole unharmed, but cannot leave it nor survive long. A Black Hole must contain a singularity. Black Holes evaporate, big ones more slowly. When a large enough star runs out of fuel, it must collapse to a Black Hole?

The Universe - the Big Bang, inflation?, expansion/crunch?, flatness?, dark matter/energy?, cosmology?.

Galaxies - Always black holes at their centres?

The Milky Way - our Galaxy - centre in Sagittarius, a supermassive black hole (Sgr A*) orbited by many star-sized ones within ~ 1 pc.

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