Chapter 10: Review

The chapter problem, solved

The telescope orbits the Earth once every 95 minutes, about 540 km above the ground. Radio signals from it travel at $3.0 \times 10^{8}\,\text{m/s}$ . It photographs star-forming clouds and distant galaxies whose light is red-shifted.

1. What keeps the telescope in orbit. Gravity provides a force of attraction between the telescope and the Earth. The force is directed towards the centre of the Earth. This force changes the direction of the telescope all the time, so its path curves into a circle. Without gravity, the telescope would travel in a straight line away into space.

2. Why the telescope does not fall. The telescope is moving sideways as it falls. The pull of gravity and its sideways motion together keep it falling around the Earth instead of into it. It is never above gravity: gravity acts between all masses, so the Earth pulls on the telescope even at that height. The pull is weaker than at the ground, but it is not zero.

3. Velocity in the orbit. The telescope moves at a constant speed, but its direction changes all the time. Velocity is speed in a given direction, so the velocity changes even though the speed does not. A stable orbit needs a speed that matches its radius. If the speed changed, the radius would have to change until the two matched again.

4. The time for a radio signal to reach the ground. The height is 540 km, which is $5.4 \times 10^{5}\,\text{m}$ .

\begin{aligned} t &= \frac{d}{v} \\ &= \frac{5.4 \times 10^{5}}{3.0 \times 10^{8}} \\ &= 1.8 \times 10^{-3}\,\text{s} \end{aligned}

The signal takes $1.8 \times 10^{-3}\,\text{s}$ , or 1.8 ms, to reach the ground.

5. Why a star such as the Sun is stable. Fusion reactions in the core release energy, which pushes outwards and tends to make the star expand. Gravity pulls the material inwards and tends to make it collapse. The outward push and the inward pull are equal, so the star is in equilibrium. It keeps the same size and shines at a steady rate.

6. The life cycle of a star the size of the Sun. It forms from a cloud of dust and gas pulled together by gravity. Fusion starts, and the star becomes a main-sequence star. Later it expands into a red giant, then cools and collapses into a white dwarf. Fusion in stars makes the elements up to iron. Elements heavier than iron are made in a supernova.

7. The red-shift of the distant galaxy. The light from the galaxy has a longer wavelength than the same light made in a laboratory. The dark lines in its spectrum are moved towards the red end. This shows that the galaxy is moving away from us. The further away a galaxy is, the faster it is moving away, which is evidence that the universe is expanding.

8. How long the light has travelled. The galaxy is $2.4 \times 10^{25}\,\text{m}$ from the Earth.

\begin{aligned} t &= \frac{d}{v} \\ &= \frac{2.4 \times 10^{25}}{3.0 \times 10^{8}} \\ &= 8.0 \times 10^{16}\,\text{s} \end{aligned}

\begin{aligned} t &= \frac{8.0 \times 10^{16}}{3.15 \times 10^{7}} \\ &= 2.5 \times 10^{9}\,\text{years} \end{aligned}

The light has travelled for about 2.5 billion years. We see the galaxy as it was 2.5 billion years ago, not as it is now.

9. How red-shift supports the Big Bang model. The Big Bang model says the universe began from a very small region that was extremely hot and dense, about 13.8 billion years ago, and has been expanding ever since. Red-shift shows that the universe is expanding, so the observations match the model. The cosmic microwave background radiation is further evidence: it is left over from the hot, dense early universe.

10. What is still not understood. Since 1998, distant supernovae have suggested that the expansion of the universe is speeding up. The cause is not known. It is called dark energy, and dark matter is also not understood. This final judgement is a reasoned answer. A computer cannot check it, so compare your reasoning with the evidence above.

Mixed practice — choose the method first

For each question, say which equation or idea you will use before you calculate. Keep your units with your numbers.

The telescope orbits 540 km above the Earth. A radio signal travels at $3.0 \times 10^{8}\,\text{m/s}$ . Calculate the time for a signal from the telescope to reach the ground.
Explain what keeps the telescope in a circular orbit around the Earth, and describe the direction of the force.
The telescope photographs new stars forming. Explain why a star such as the Sun stays the same size for billions of years.
The telescope photographs distant galaxies. Explain what is meant by the red-shift of the light from a galaxy, and what it shows.
State what the Big Bang model says about the start of the universe, and explain how red-shift supports it.
One of the galaxies photographed by the telescope is $2.4 \times 10^{25}\,\text{m}$ from the Earth. Say which equation you will use, then calculate how long the light has taken to reach the Earth. Give your answer in seconds to 2 significant figures.
State the main features of our solar system, and say where the solar system sits in the universe.
H The telescope moves at a constant speed in its orbit, but its velocity changes. Explain how this is possible.
H A small force from a thruster changes the speed of a satellite in a stable circular orbit. Explain why the radius of the orbit must change.
A space probe travels $1.2 \times 10^{8}\,\text{m}$ in $4.0 \times 10^{2}\,\text{s}$ . Say which equation you will use, then calculate its average speed. Give your answer to 2 significant figures.
A radio signal from a satellite has a frequency of $6.0 \times 10^{14}\,\text{Hz}$ and a wavelength of $5.0 \times 10^{-7}\,\text{m}$ . Calculate the speed of the signal. Give your answer to 2 significant figures.
A satellite of mass 1500 kg orbits at a speed of 20 m/s at one point in a transfer orbit. Calculate the energy in its kinetic store. Give your answer to 2 significant figures.
An astronaut has a mass of 70 kg. The gravitational field strength on the Moon is 1.6 N/kg. Calculate the weight of the astronaut on the Moon. Give your answer to 2 significant figures.
Fusion happens in the core of a star such as the Sun. Describe the process of nuclear fusion and explain why it releases energy.
A television programme makes two claims: that a satellite stays in orbit because the Earth pulls on it, and that the universe is expanding because distant galaxies are red-shifted. Say which idea supports each claim, and explain each one in one sentence.

Answers and concise solutions

1. Time for the telescope signal to reach the ground

Answer: $540\,\text{km} = 5.4 \times 10^{5}\,\text{m}$ . $t = \dfrac{5.4 \times 10^{5}}{3.0 \times 10^{8}} = 1.8 \times 10^{-3}\,\text{s}$ , which is 1.8 ms.

2. What keeps the telescope in orbit

Gravity provides a force of attraction between the telescope and the Earth.
The force is directed towards the centre of the Earth.
The force changes the direction of the telescope, so its path curves into a circle instead of a straight line.

3. Why a star stays the same size

Fusion reactions in the core release energy, which pushes outwards and tends to make the star expand.
Gravity pulls the material of the star inwards and tends to make it collapse.
The outward push and the inward pull are equal, so the star is in equilibrium and stays the same size.

4. Red-shift and what it shows

The wavelength of the light is longer than the wavelength of the same light measured in a laboratory.
The red-shift shows that the galaxy is moving away from the Earth.
The further away a galaxy is, the faster it is moving away, which is evidence that the universe is expanding.

5. The Big Bang model and the evidence

The universe began from a very small region that was extremely hot and dense.
The universe has been expanding ever since.
Red-shift shows that the galaxies are moving apart, so the universe is expanding. This is evidence that supports the Big Bang model.

6. Time for the light from the distant galaxy

Answer: Use $\text{time} = \dfrac{\text{distance}}{\text{speed}}$ . $t = \dfrac{2.4 \times 10^{25}}{3.0 \times 10^{8}} = 8.0 \times 10^{16}\,\text{s}$ , which is about $2.5 \times 10^{9}$ years. We see the galaxy as it was 2.5 billion years ago.

7. The main features of the solar system

The solar system has one star, the Sun.
Eight planets orbit the Sun, and dwarf planets also orbit the Sun.
Natural satellites, called moons, orbit the planets.
Artificial satellites built by people also orbit the Earth and other bodies.
The solar system is a small part of the Milky Way galaxy, which contains billions of stars.

8. How the velocity changes while the speed stays the same

Velocity is speed in a given direction.
The direction of the telescope changes all the time as it goes round the orbit.
The speed stays the same, but the changing direction means the velocity changes.

9. Why the radius of a stable orbit must change

A stable circular orbit needs a speed that matches its radius.
When the speed changes, the satellite can no longer stay in a stable orbit at the same radius.
The radius must change until the speed and the radius match again, so the orbit is stable at the new radius.

10. Average speed of the space probe

Answer: Use $\text{speed} = \dfrac{\text{distance}}{\text{time}}$ . $v = \dfrac{1.2 \times 10^{8}}{4.0 \times 10^{2}} = 3.0 \times 10^{5}\,\text{m/s}$ .

11. Speed of the radio signal

Answer: Use the wave equation $v = f\lambda = 6.0 \times 10^{14} \times 5.0 \times 10^{-7} = 3.0 \times 10^{8}\,\text{m/s}$ . This is the speed of light in a vacuum, which is what we expect for a radio wave.

12. Energy in the kinetic store of the satellite

Answer: $E_k = \tfrac{1}{2}mv^2 = 0.5 \times 1500 \times 20^2 = 300000\,\text{J}$ , so $3.0 \times 10^{5}\,\text{J}$ to 2 significant figures.

13. Weight of the astronaut on the Moon

Answer: $W = mg = 70 \times 1.6 = 112\,\text{N}$ , so $1.1 \times 10^{2}\,\text{N}$ to 2 significant figures. The mass is still 70 kg, because mass does not change with position.

14. Fusion in a star

Fusion joins two light nuclei, such as hydrogen nuclei, to form a heavier nucleus, such as helium.
Some of the mass is converted into the energy of radiation, which is why energy is released.
The core of a star is hot and dense enough for this to happen continuously.

15. The idea behind each claim

The first claim uses gravity. Gravity provides the force towards the centre of the orbit, which bends the path of the satellite into a circle.
The second claim uses red-shift. The wavelength of the light from a receding galaxy is longer, and the further away a galaxy is the faster it recedes, which is evidence that the universe is expanding.

What you can now do

describe the main features of the solar system, including the planets, the dwarf planets, the moons and the artificial satellites;
compare a planet, a moon and an artificial satellite;
explain how gravity keeps a planet or a satellite in a circular orbit;
explain how the Sun formed from a cloud of dust and gas, and why fusion reactions keep it stable;
describe the life cycle of a star the size of the Sun and of a much more massive star;
explain why the light from distant galaxies is red-shifted;
explain how red-shift is evidence that the universe is expanding, and how it supports the Big Bang model;
describe the cosmic microwave background radiation as evidence for the Big Bang;
calculate how long light takes to travel a given distance.

Your relevance reflection

Return to the prompt from the chapter opener: where have you seen or used something to do with space? Write one more example now that you have finished the chapter. Has the chapter changed what you notice about a satellite, a weather forecast or a photograph from a space telescope?