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Granulation is due to the convection operating below the photosphere.


The grainy appearance of the solar photosphere is produced by the tops of these convective cells and is called granulation.


Convection is the technical term for heat transport by overturning fluid or gas. We can observe convection in daily life: boiling is an example of transporting energy by convection.

This convection produces columns of rising gas just below the photosphere that are about 700 to 1000 km in diameter.

In these columns hot fluid rises up from the interior in the bright areas, spreads out across the surface, cools and then sinks inward along the dark lanes.


A typical granule lasts about 8 to 20 minutes. At one time, the sun's surface is covered by approx 3.5-4 million granules.


The granulation pattern is continually evolving as old granules are pushed aside by newly emerging ones. See this GIF for more accurate understanding of this statement:



#3380" N"#. Don't try this at home: you might get torn apart (see the explanation).


The amount of tension is given by the difference in gravitational force between the two masses. Let A and B be the masses, with A being closer to the black hole O. Then:



As the A and B masses are equal we substitute #M_A# for #M_B# and subtract to get the tension:


Now put in numbers and calculate:

#G=6.67xx10^{-11}" Nm"^2/"kg"^2# (same units in SI system as those given)

#M_A(=M_B)=1" kg"#, taken as exact values

#r_A=686,000-0.5=685,999.5" m"#

#r_B=686,000+0.5=686,000.5" m"#


#T=3380" N"#. This is over 170 times the gravity of Earth on the same amount of mass. A similar 100-g+ force acting on your mass would pull you apart, even though you are still relatively far from the hole's horizon.


Spectroscopy is measuring light to find out what something is made of on an atomic scale.


Spectroscopy is measuring the light emitted by stars to tell what sort of atoms the star is making, or what a substance is made up of.

Each atom is a nucleus surrounded by a load of electrons. The electrons have specific energy levels, like stairs, and can move between the levels by absorbing or emitting photons of certain frequencies.

When an electron absorbs a photon, it gains energy and moves up the stairs. When it emits a photon, it loses energy and moves down the stairs again. Luckily for us, photons are also light, so we can see it when electrons lose energy in atoms.

Also, each atom has very specific energy levels that we can measure precisely here on Earth, so we know from the frequency of light emitted what energy is lost and so what atom it is in the star, or any other substance.


[The above image is an example of spectroscopy.]

Energy of a photon is given by:

#E=hf# or #E=hnu#

where #h# is called Planck's constant and is approximately #6.626*10^-34##J.s#, and #f# is the frequency of the light emitted in Hertz (oscillations per second).

We may not be able to directly measure the frequency, but we know that the speed of light is constant and that it is given by:

#c = flambda#

where #c# is the speed of light, #lambda# is wavelength, and #f# is, again, frequency. The speed of light is about #3*10^8m/s# approx. The real value is taken as #2.99792458*10^8m/s#. These values are speed of light in a vacuum.


#f=c/lambda#, so


This is great because the colour of light is how humans see wavelength, so just from the colour of something we can determine the energy of light emitted, and the energy of light emitted is specific to each atom.

We can also go the other way, rather than measuring the light that something emits, measure the light that it absorbs, which, although it is exactly the opposite, gives us exactly the same result. We can do this by shining white light on a gas in the lab and seeing what light comes through the other side. The light that doesn't come through is absorbed, and from this we can tell precisely what the gas is.


A star is in hydrostatic balance if there is a force which can counter gravitational collapse.


In the case of main sequence stars, gravitational collapse is balanced by radiation pressure from the fusion reactions taking place in the star's core.

When a star of less than 8 solar masses has consumed all of the hydrogen and helium in its core, it can't achieve the temperatures and pressures required to start carbon fusion. At this point the star's carbon/oxygen core collapses into a white dwarf. In this case further gravitational collapse is held in balance by electron degeneracy pressure. This is a quantum effect which forbids two electrons being in the same state.

In larger stars fusion reactions created heavier elements until the core is mainly iron. Iron fusion requires more energy than is released. Once fusion reactions stop, the iron core collapses under gravity. In this case electron degeneracy pressure is not strong enough to stop gravitational collapse. The core collapses into a neutron star. Gravitation collapse in a neutron star is balanced by neutron degeneracy pressure which prevents two neutrons being in the same quantum state.

If the core has a mass of more than a few solar masses, neutron degeneracy pressure is not strong enough to stop gravitational collapse. The core collapses further into a black hole. In this case there is no balance as gravity has won. We don't really understand black holes as our laws of physics break down. General Relativity predicts that inside the black hole is a singularity which is a point of infinite density where all of the mass of the black hole resides.


Antimatter is matter made up from particles with the opposite charge to normal matter.


Most particles have an anti-particle. In particular charged particles have an anti-particle with the opposite charge. Some uncharged particles are their own anti-particle.

Normal matter consists of mainly protons, neutrons and electrons. The proton is positively charge and the antiproton is negatively charged. The electron is negatively charged and the antielectron, or positron, is positively charged. The neutron and the anti-neutron have neutral charges.

Antimatter is made up of antiprotons, antineutrons and positrons.


When a particle meets its antiparticle they annihilate each other to form photons.

When the universe was formed there should have been equal amounts of matter and antimatter. For reasons unknown, matter was more dominant. Although it is possible that there may be antimatter galaxies.

We don't know much about the properties of antimatter. We do know that the antiparticles exist and behave in the same way as the normal particles except for charge. It is now possible to form small quantities, upt to a few hundred atoms of anti-Hydrogen, in the laboratory and more experiments can now be conducted.

Richard Feynman showed that mathematically a positron is indistinguishable from an electron travelling backwards in time. This doesn't mean that antimatter travels backwards in time, it is just a consequence of the mathematics.


The gravitational parameter for a body #GM# is the gravitational constant #G# multiplied by the mass of the body.


When doing calculations involving gravity, the gravitational constant #G# is required. It is however difficult to measure the value of #G# to high degrees of accuracy.

The known value of #G=6.674 08 \times 10^-11 m^3 kg^-1 s^-2# but the uncertainty in the value is #0.000 31 \times 10^-11#. So, effectively we only know the value of #G# to four decimal places.

Calculating the mass #M# of a body, such as a planet or the Sun, is also difficult. To do so accurately would require knowledge of the body's volume and density which we can't know accurately.

Fortunately, in gravitational equations the quantities #G# and #M# are multiplied together to form the gravitational parameter #\mu=GM#.

Using data from measurements of the orbits of planets, moons and satellites it is possible to measure the value of the gravitational parameter for bodies with a high degree of accuracy. The values of the gravitational parameter for the Sun, Earth and other planets have been carefully measured.

So, if you want to calculate the orbital parameters of a satellite orbiting the Earth, you don't get the values for #G# and #M# and multiply them together. Instead you get the much more accurate gravitational parameter #\mu# for the Earth.

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