Gravity and Sun Size


Comparison of the current-day Sun and the Sun as a red giant in the future. by
Oona Räisänen. 2007.

Gravity as the Driving Force

The Sun has a mass of 2 * 10^30 kg. Gravity exerts a compression force on the Sun proportional to this immense mass. So why doesn’t the sun collapse under the weight of its gravity?

The pressure of the center of the Sun is about 340 billion times the air pressure on Earth at sea level. Temperatures at the Sun’s core reach 15 million Kelvin. The conditions at the Sun’s core allow nuclear reactions to occur.

We will leave the exact reactions for a different time. Nevertheless, the basic reaction for stars the size of our Sun is called the proton-proton chain:

 4{_{1}^{1}\textrm{H}}\rightarrow{^{1}\textrm{He}^{2-}}+2e^{+}+2v_{e}

The nuclear reactions inside the core result in energy and an outward pressure that combats the inward pressure of gravity. Gravity is the driving force behind the nuclear reactions that power the Sun, which in turn determines its size.

Hydrostatic Equilibrium

While the core of the Sun is able to fuse hydrogen into helium, the size of the Sun will be relatively stable. The outward pressure of the reaction matches the inward force of gravity exerted on a star proportional to its mass.

During this period, the Sun is in “Hydrostatic Equilibrium” along the main sequence. Eventually, the Sun’s core will run out of hydrogen to fuse. The core will begin to contract and core temperatures will increase.

Red Giants

Once the core of the Sun runs out of hydrogen material to fuse, the core will begin to collapse. The extreme temperature and pressure caused by the core collapsing allows layers of hydrogen just outside the core (which previously had no role in nuclear fusion) to begin reactions. This outer layer contains more volume. Additionally, the star uses a different fusion reaction that results in the star producing much greater net energy.

The Sun will expand and become a Red Giant due to the greater outward pressure exerted as a response to the force of gravity collapsing the star.

Post-Red Giant

Our Red Giant Sun will eventually lose much of its mass and its emitted material will become a planetary nebula. It will become a white dwarf and slowly cool.

Gravity initiates the process that forms nebulae and stars, influences the formation and size of the star, and determines the life cycle and death of the star. In this way, gravity is the catalyst for change, and the driving force, in the life of our Sun.

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How Much Does Light Weigh?

Light is made of photons. And photons are massless particles, which means they have no invariant/resting mass. Therefore, light has no mass and no weight. End of story, right?

The Force of Light

Did you know that light exerts pressure on objects? This force can even increase an objects weight, albeit to a small degree. For instance, Vsauce explains how much a landmass might weigh covered in sunlight (for the city of Chicago, sunlight only adds 300 lbs).

Michael Stevens from Vsauce describes the weight of light. Octover 7, 2012. Youtube. For the section we discuss, please watch up to 0:56.

Although insignificant on a small scale, scientists must account for this force – called radiation pressure or solar radiation pressure – in planing space missions.

Solar radiation pressure plays a role in the formation of galaxies, stars and clusters, and solar/planetary systems. Additionally, solar radiation shapes the tails of comets.

A Common Misconception

Light carries energy and momentum. We know that energy, momentum and mass are related. Can we assume that light also has mass?

E = mc^{2}

This misconception stems from Einstein’s mass-energy equivalence formula. Einstein proposed that an object with energy has an equivalent amount of mass. Einstein’s formula only applies to objects with invariant/resting mass. Since photons have no resting mass, we have to use a different formula:

E = pc

where p is the momentum of the particle. Therefore, we can observe momentum and energy for massless particles.

tl;dr Light does not have weight or mass. Light can push an object or increase its weight, to a minimal degree.

We Weigh Less in the Dark, technically

Do we actually weigh more in sunlight? Functionally, no. But, we can still estimate an upper bound.

First, solar radiation pressure is applied to objects in the direction of sunlight. For this problem, let us pretend that we are shaped like rectangular solar panels.

Second, we learned from Vsauce that light exerts a force of pressure on the surface of Earth of about 1e-9 lbs per square inch. Considering the average human has a surface area of 1.9 meters squared, we can calculate the following:


  \frac{1.0*10^{-9} lbs}{in^{2}}  * \frac{1550 in^{2}}{m^{2}}\  * 1.9m^{2}

 = 3.0 * 10^{-6}lbs

So the next time you weigh yourself, turn off the lights. You might not notice a difference, but you just shaved a couple millionths of a pound.

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