Physics
Double Award
Double Award
Cambridge IGCSE
TOPIC 6: SPACE PHYSICS
Stars in the night sky look small and distant. However, stars are enormous - typically far bigger than planets like the Earth. This excellent video gives a comparison of the size of planets and stars:
YouTube video: Star size comparison
From morn1415
The video makes you realise that - even though our own sun is enormous compared to Earth -there are other stars out there that are much, much larger. The other aspect of this video that is important is that stars have many different colours, ranging here from red and orange, to white and blue. This is because the stars all have a different temperature at the surface. Can you guess which colour stars are the hottest? The colour of the star indicates the temperature. Red stars are not as hot as orange stars. Then comes yellow/white, white, and finally blue stars that are extremely hot at the surface.
Extension
The colour of stars follows the general order of the spectrum, from the red end to the blue end. Why is it that there are no green or violet stars? See if you can find out, or click here for hints.
A red giant star actually gives out a range of frequencies, including a lot of infra-red and red light, and a little orange / yellow etc. However, to our eyes, the main colour seen is red. What colour would a star look like if it gave out a fairly balanced spread of the colours from the spectrum, centred on green?
The Sun is a yellow/white star of medium size, consisting mostly of hydrogen and helium, and it radiates most of its energy in the infrared, visible and ultraviolet regions of the electromagnetic spectrum. The Sun produces all of this heat and light through a process known as nuclear fusion.
It is just one star in a giant spiral galaxy called the Milky Way, consisting of many billions of stars. We can see other galaxies of similar size to ours - figure 1 shows our neighbouring galaxy called Andromeda, which is of a similar size and shape to our own Milky Way galaxy:
Figure 1: A typical spiral Galaxy like the Milky Way (The Andromeda Galaxy)
David (Deddy) Dayag CC BY-SA 4.0
The distances between stars in our galaxy is enormous. On this scale, using the meter as the basic unit of distance is a bit small! Astronomers use a unit called the light-year. This is simply the distance light can travel (in a vacuum) in a year. As light travels incredibly fast, a light-year is a very large distance - about 10 thousand billion kilometres!
The Sun is only about 8 light-seconds from Earth, whereas the distance to the nearest stars to our solar system is about 4 light-years. Stars are much further apart in galaxies than the planets are in our Solar System.
The planets orbit the Sun in near circular orbits. The Sun contains most of the mass of the entire solar system, which is why the planets go around the Sun.
Did you know that Mercury is the closest planet to the Sun, and also has the fastest orbital speed? The further away from the Sun a planet is found, the lower the orbital speed. Different orbital paths have a speed that is fixed by the force of gravity at that point. As Mercury is close to the Sun, it experiences a stronger gravitational field than the Earth, and this means it orbits at a higher velocity.
Notice that in the simulation shown here in fig. 6, the inner planet overtakes the outer planet, and it is actually travelling significantly faster due to the higher gravitational field strength close to the blue star.
Figure 6: Simulation of 2 planets in orbit
GRC NASA
Note that as gravity pulls on a planet or moon during a circular orbit, it makes the direction change, but not the speed. This change in direction leads to a change in the velocity, as velocity is a vector quantity. (See section 1.1 for a recap about vectors). Therefore the velocity changes, but not the speed of the orbit.
Questions:
1. Explain why the planets Saturn and Neptune are travelling at different speeds around the Sun.
Saturn and Neptune are in different orbits. (Neptune is much further from the Sun). The gravitational field strength from the Sun is weaker for Neptune than Saturn, and causes it to orbit at a much slower speed than Saturn.
As Neptune orbits at a much slower speed than Saturn, and also has much further to travel, so the time period for 1 orbit is MUCH longer than the time period for Saturn as shown in the data table.
For the near circular orbits of moons and planets it is pretty straightforward to work out a formula for the orbit speed:
| average speed = | distance |
| time |
Therefore we can replace the distance and the time in this formula to give us the speed around a circular orbit:
| average orbital speed = | 2 x π x orbital radius |
| time period |
| v = | 2 x π x r |
| T |
The speed is the average speed because, as discussed above, true orbits are ellipses and the orbital speed will change a little during the orbit. Note that there are no units given here and you will need to use some common sense. If a question gives the radius in kilometres (km) and the time in hours (h), then the speed will be in units of km/h.
Have a go at these questions to test your understanding of this formula, and the rest of this section:
Questions:
2. The Moon orbits the Earth in approximately 708 hours, with a radius of orbit of 385 000 km. Using the formula given above, calculate the average orbital velocity of the Moon.
Using the formula
| v = | 2 x π x r |
| T |
| v = | 2 x π x 385 000 |
| 708 |
3. The Hubble Space Telescope (HST) orbits the Earth at a speed of 7.6 km/s and has an orbital time period of 5700 seconds.
a) Both time period and speed include seconds, so we can substitute the numbers directly into the formula:
| v = | 2 x π x r |
| T |
| 7.6 = | 2 x π x r |
| 5700 |
| r = | 7.6 x 5700 |
| 2 x π |
b) The Earth's radius is 6400 km, so the HST's height above the Earth's surface is 6900 - 6400;
so the distance = 500 km
The Sun is the closest star to us, and we can study it to find out more about how stars produce heat and light. We now know that all stars produce heat in a process called nuclear fusion:
Heavy nuclei are held together by a strong force like a nuclear glue. This force only acts over a short range. If you can get two light nuclei close together, then this force makes them snap together like strong magnets, and this releases energy. The energy comes from a small quantity of mass that is lost in the process, and converted to energy.
This process - of light nuclei fusing together - is called nuclear fusion. It only works with light nuclei like hydrogen and helium, and only when they are put very close together. Unfortunately, these nuclei have protons in them that repel each other, so they really do not want to be close together! The electrostatic repulsion works over longer distances, so initially the protons repel unless they are forced very close together.
Fusion needs very high pressures and temperatures. This makes light nuclei move very fast and close together, causing some to fuse. This is the energy source that keeps the Sun and all stars producing heat and light! In all stars, hydrogen fuses together to make helium nuclei, and this happens for millions or billions of years. The temperature needed to do this for hydrogen in stars is millions of degrees Celsius, and even then the process is slow.
Where do stars come from? Do stars like the Sun last forever?
Stars produce heat and light through nuclear fusion. However, this process cannot last forever, and eventually the star will run out of the elements needed to sustain the fusion reaction. This results in the star changing dramatically. By studying the stars around us, astrophysicists have been able to gain a better understanding of how stars evolve, from birth to final death.
The diagram in figure 3 gives an overview of the stages of a star's evolution. As you can see, there are two paths which depend on the size of the star.
Figure 3: The evolution of stars
(Not to scale)
First of all, we will look at the stages for stars similar to the Sun:
All stars begin from a humble cloud of interstellar (between stars) gas and dust, called a nebula. If the mass of a region of the nebula is large enough, gravity begins to pull the nebula together and compress it.
As the gases collapse inwards and gravity compresses them, they heat up and form a protostar. This kind of star is not yet big enough or hot enough for fusion reactions to begin, and it stays in this state as more gases fall inwards and the star grows in mass and gets hotter.
Eventually the gas has been compressed so much that the temperature reaches millions of degrees Celsius, enough for a fusion reaction to begin. A star is born! A protostar becomes a stable star when the
inward force of gravitational attraction is
balanced by an outward force due to the high
temperature in the centre of the star. The fusion reaction lasts for a long time - billions of years for a star like the Sun. Hydrogen is slowly converted to helium in fusion reactions. Nearly all of the stars we see in the night sky are these 'middle -aged' stars, and are called main sequence stars. During this stage, the inwards force of gravity on the star is balanced by the outwards forces due to high pressures and temperatures caused by fusion reactions. The star remains stable.
When a star begin to run out of hydrogen, more complicated fusion reactions can start. Elements heavier than helium are formed as nuclei fuse together, including carbon and oxygen. The star begins to swell outwards and cool a little at the surface, producing red giant stars.
(If you are interested, a normal red giant stops there, and cannot fuse elements heavier than oxygen as it is not hot enough).
This red giant, Aldebaran is almost the same mass as the Sun, but is now in the red giant phase of its evolution. At some point, our own Sun will expand to a similar size.
Figure 4: The red giant Aldebaran
When the last of the fusion reactions stops, the star shrinks. Some of the outer layers of hydrogen and helium escape into space to form a new nebula around the star. This nebula is called a planetary nebula, only because it looked like a planet to the early astronomers, In reality, it has nothing to do with planets!
As the remaining star core shrinks inwards, the compressed gases heat up making the star white hot at the surface, but very small. This is called a white dwarf star, and it will stay this way until the star eventually radiates the last of its heat energy away into space.
Figure 5: The 'ring' nebula: A planetary nebula with a white dwarf in the centre
NASA, ESA and the Hubble Heritage (STScI/AURA)-ESA/Hubble Collaboration
Stars with a mass much higher then the sun will be extremely bright and will convert hydrogen at a vast rate through fusion reactions. They follow the same stages, from nebula to protostar and then main sequence star. When the hydrogen runs out, they also swell up to make red giant stars, but these are so large they are classed as red supergiant stars.
A red super giant has a core that is so hot, that fusion continues making heavier and heavier nuclei, from carbon to oxygen, and onwards to the element iron. Once iron is formed, fusion cannot continue. (The reasons for this are complicated and beyond the requirements of the syllabus). The core has run out of fuel.
Once a red supergiant runs out of fuel to sustain the complicated fusion reactions that occur, the star collapses very rapidly. As it rushes inwards, it heats up to enormous temperatures causing nearly all the remaining fusion reactions to occur at once. Outer layers of hydrogen, helium and other light elements fuse extremely rapidly. The star explodes in a flash releasing so much energy, it can out-shine an entire galaxy! This explosion is called a supernova. The core remnant that is left continues to collapse inwards.
During a supernova explosion, fusion reactions continue as so much additional energy is available and the temperature is so high. Elements heavier than iron are formed as heavy nuclei fuse together. All of the naturally occurring elements we find on Earth and in our Solar System were created by stars, and the heavier elements created in supernovas. The Solar System was literally made from star dust - the remnants of a previous supernova reaction nearby.
Supernova explosions distribute these heavier elements throughout the universe. The remaining nebula can form new solar systems with stars and planets, and astronomers are certain that this is how our own Solar System was formed.
The remaining core collapses into a tiny, extremely dense core made of neutrons, called (surprisingly) a neutron star.
If the core remnant has a huge mass, it collapses inwards to a point. Nothing can stop the collapse. This is where things get very weird, as the star is still there, with a high mass and strong gravity, but it is effectively a point in space. This is called a black hole.
There was a supernova visible from Earth in the year 1054, and the image shown in figure 6 shows the remnants of the exploded star. There is a neutron star somewhere in the centre of this vast cloud of gas.
Questions:
4. The Sun is currently a main sequence star, in the middle of its evolutionary path.
Describe the next stages in the evolution of stars like the Sun.
5. Very large main sequence stars will eventually run out of hydrogen in the star's core. Describe the next stages in a the life cycle of a star.
A very large main sequence star will:
6. Explain what is meant by a nebula.
A nebula is a large cloud containing gases (like hydrogen and helium) / dust.
7. Most of the universe consists of hydrogen. Our Solar System contains many other heavier natural elements.
a) Elements heavier than hydrogen are formed in fusion reactions inside stars. (Main sequence stars create helium, and red giants / super giants are responsible for the creation of elements heavier than helium, up to iron).
b) Elements heavier than iron are created in supernovas.
Now test your understanding using these quick, 10 minute questions on Stars:
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