Stars and the Universe

Composition and Energy Source
The Sun is a star of medium size, consisting mostly of hydrogen and helium. It radiates most of its energy in the infrared, visible light, and ultraviolet regions of the electromagnetic spectrum.

In stable stars (including the Sun), the energy is powered by nuclear fusion. Specifically, hydrogen nuclei fuse together to form helium. This process releases vast amounts of energy.

Building on the concept of forces, a star remains stable when two opposing forces are balanced:

1. Inward force: Gravitational attraction pulls the star's mass inward.
2. Outward force: The high temperature in the core (due to fusion) creates pressure that pushes outward.

When these forces are equal, the star is in a stable state.

Structure of the Universe

• Galaxies are huge systems made up of many billions of stars.
• The Sun is a star in the galaxy known as the Milky Way.
• Other stars that make up the Milky Way are much further away from the Earth than the Sun is from the Earth.
• The Milky Way is one of many billions of galaxies making up the Universe.
• The diameter of the Milky Way is approximately 100,000 light-years.

Redshift
When we observe light from distant galaxies, the wavelength appears longer (shifted towards the red end of the spectrum) compared to light emitted on Earth. This is called redshift.

• Redshift occurs because the galaxy is receding (moving away) from us.
• The greater the distance to the galaxy, the greater the redshift.
• This observation is evidence that the Universe is expanding.
• This supports the Big Bang Theory, which states that the Universe began as a single point and has been expanding ever since.

Formation

1. A star forms from interstellar clouds of gas and dust containing hydrogen.
2. The cloud collapses under its own gravitational attraction, causing the temperature to rise. This collapsing cloud is called a protostar.
3. When the core becomes hot enough, nuclear fusion begins (hydrogen fusing into helium). The outward pressure from fusion balances the inward gravitational force, and the star becomes stable.

Evolution
All stars eventually run out of hydrogen fuel in their cores.

1. Less Massive Stars (like the Sun):

   • Expand to form a Red Giant.
   • Eventually shed their outer layers to form a planetary nebula.
   • The core remains as a hot, dense White Dwarf.

2. More Massive Stars:

   • Expand to form a Red Supergiant.
   • Explode as a Supernova, forming a nebula containing hydrogen and new heavier elements.
   • The core collapses further:
     • If the core is massive enough, it forms a Neutron Star or a Black Hole.

Recycling
The nebula from a supernova contains heavy elements and may form new stars with orbiting planets.

Calculating Speed from Redshift
The speed v at which a galaxy is moving away from Earth can be found from the change in wavelength of its starlight due to redshift. The relationship is:

\frac{v}{c} = \frac{\Delta \lambda}{\lambda_0}

Where:

• v = speed of the galaxy (m/s)
• c = speed of light (3.0 \times 10^8 m/s)
• \Delta \lambda = change in wavelength (observed wavelength - original wavelength)
• \lambda_0 = original wavelength measured on Earth

Hubble Constant (H_0)
The Hubble constant is the ratio of the speed at which a galaxy is moving away to its distance from Earth.

H_0 = \frac{v}{d}

Where:

• H_0 = Hubble constant (s⁻¹)
• v = recession speed (m/s)
• d = distance (m)

The current estimate for H_0 is 2.2 \times 10^{-18} s⁻¹.

Age of the Universe
The equation \frac{d}{v} = \frac{1}{H_0} represents an estimate for the age of the Universe. This implies that all matter was present at a single point in the past.