Topic 07 | Earth and space sciences

Space exploration

Year 10 (Levels 9-10 band): telescopes and their discoveries, rocket propulsion and orbits, crewed missions, satellite applications, and the challenges of living beyond Earth.

55-75 min Printable practice Answer key Challenge included
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Read the explanation, work through the examples, then complete the core practice before printing.

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What you will learn

Worked example 0 Real-world example: GPS and relativity

Your phone uses timing signals from four GPS satellites to triangulate your position. GPS satellites orbit at 20200\sim 20\,200 km and travel at 14000\sim 14\,000 km/h. Why must the satellite clocks be corrected relative to Earth’s clocks for GPS to work?

  1. Each satellite broadcasts the time at which its signal left.
  2. The phone calculates its distance from each satellite: d=c×Δtd = c \times \Delta t, where cc is the speed of light.
  3. A timing error of just 11 microsecond would produce a position error of c×106300c \times 10^{-6} \approx 300 m.
  4. Relativity predicts the satellite clocks tick at a slightly different rate (by about 3838 microseconds per day) compared with ground clocks, due to velocity and weaker gravity.
  5. Without correcting this, positions would drift 10\sim 10 km per day — useless for navigation.

Key idea: modern space applications rely on extraordinary precision in physics. GPS is a daily demonstration of Einstein’s relativity.

1. Telescopes and discovery

Different wavelengths reveal different physics:

Worked example 1 Why is the James Webb Telescope in space?

Give two reasons the James Webb Space Telescope operates at L2 rather than on Earth.

  1. Earth’s atmosphere blocks most infrared light (absorbed by water vapour and CO2_2), so ground-based IR telescopes work only at narrow wavelengths.
  2. L2 is far enough from Earth and the Sun that the telescope sun-shield keeps the detectors at 233C-233\,^\circ\text{C}, essential because a warm telescope would emit its own IR and drown out faint signals from distant galaxies.

(Additionally, L2 is a gravitationally stable point where minimal fuel is needed to stay in position.)

2. Rockets and orbits

Rocket propulsion: a rocket pushes hot exhaust gases backward. By Newton’s third law, the gases push the rocket forward. The faster and heavier the exhaust, the greater the thrust.

Getting to orbit: a rocket must reach a horizontal speed of 7.8\sim 7.8 km/s (28000\sim 28\,000 km/h) at low-Earth-orbit altitude. At that speed, the vehicle falls toward Earth at the same rate the Earth’s surface curves away beneath it — continuous free-fall, which is what “being in orbit” means.

Orbit types:

Worked example 2 Apparent weightlessness on the ISS

Astronauts on the International Space Station float, even though gravity there is still 90%\sim 90\% of Earth’s surface gravity. Explain.

  1. The ISS orbits at 400\sim 400 km altitude, moving at 7.7\sim 7.7 km/s horizontally.
  2. Both the station and the astronauts are in continuous free-fall toward Earth.
  3. Since everything in the station falls at the same rate, no support force is felt — the astronauts appear weightless.
  4. Gravity is not absent — it is what keeps them in orbit. “Microgravity” is a more accurate term.

Key idea: orbit is free-fall that never hits the ground because the surface curves away as fast as the object falls.

3. Crewed missions and milestones

Worked example 3 Why Mars missions are hard

A one-way trip to Mars takes 7\sim 7 - 99 months. List three physical challenges crews will face that Moon astronauts did not.

  1. Radiation: no protective magnetic field on the way; cosmic rays and solar flares accumulate a dangerous dose over many months.
  2. Microgravity: Apollo missions were short (<2<2 weeks); Mars crews will spend 18\sim 18 months in microgravity or Martian 0.38g0.38g. Bone and muscle loss are severe.
  3. Resupply and rescue: communication with Earth has a 20\sim 20-minute one-way delay; a sick astronaut cannot be evacuated home.

(Also: psychological isolation, food and water recycling, dust toxicity.)

4. Satellites and applications

ApplicationOrbitHow it works
GPSMEOfour satellites’ timing signals triangulate position
Weather imagingGEOsame satellite continuously over one hemisphere
Earth observationLEOpolar orbit images each region daily
CommunicationsGEOTV, phone, internet relayed across continents
Scientific researchvariesHubble (LEO), Webb (L2), ISS
Worked example 4 Why is a weather satellite geostationary?

Why are weather satellites usually placed in geostationary orbit rather than low Earth orbit?

  1. GEO satellites stay above the same point on Earth (2424-hour period matches Earth’s rotation).
  2. They can produce continuous video-like imaging of developing storm systems.
  3. An LEO weather satellite passes overhead for only a few minutes twice a day; GEO gives 24/724/7 coverage of an entire hemisphere.

Practice: Year 10

Fluency

Telescopes

    1. Name one advantage of space-based telescopes over ground-based ones.
    2. Why must X-ray telescopes be placed in space?
    3. What wavelength does the James Webb Space Telescope use?
    4. What kinds of objects do radio telescopes detect that optical ones cannot?
    5. Name one significant astronomical discovery made with a space telescope.
Fluency

Rockets and orbits

    1. State Newton’s third law and explain how it applies to a rocket.
    2. Roughly what orbital speed is needed at low Earth orbit?
    3. What is a geostationary orbit, and why is its altitude fixed at 36000\sim 36\,000 km?
    4. Why does an astronaut on the ISS appear weightless even though gravity is strong there?
    5. What is “escape velocity” and how does it differ from orbital velocity?
Fluency

Missions and applications

    1. Name the first human to orbit Earth and the year.
    2. In which decade did the Apollo crewed lunar missions take place?
    3. When did the ISS begin continuous crewed occupation?
    4. Name one weather satellite system and one GPS-style navigation system.
    5. Name two countries or agencies currently running crewed space programmes.
Reasoning

Explain and justify

    1. Explain why a rocket’s fuel is 85%\sim 85\% of its launch mass.
    2. Why do most rockets carry both fuel and oxidiser, even though there is plenty of oxygen in the lower atmosphere?
    3. Explain why a single GPS satellite is not enough to give your location — the phone needs at least four.
    4. Why is radio astronomy often done in remote locations (outback Australia, Atacama desert)?
    5. Compare the dangers of a Moon mission with a Mars mission. Which mission poses greater risks, and why?
Problem solving

Apply

    1. A GPS satellite orbit altitude is 2020020\,200 km. Earth’s radius is 6400\sim 6\,400 km. What is the satellite’s distance from Earth’s centre? If the satellite moves at 1400014\,000 km/h, how long does a signal take to reach you (use c=3.0×105c = 3.0 \times 10^5 km/s)?
    2. The Apollo missions sent crews a distance of 384000\sim 384\,000 km to the Moon. At a travel speed of 5500\sim 5\,500 km/h (average), estimate the travel time in days.
    3. A geostationary satellite broadcasts a TV signal. The signal reaches the ground after 0.12\sim 0.12 s. Estimate the satellite altitude using d=ctd = ct. Does this match 3600036\,000 km?
    4. Explain why Mars landing missions must launch during specific “windows” every 26\sim 26 months.

Challenge

Reasoning

Harder reasoning

    1. The rocket equation is Δv=veln(m0/mf)\Delta v = v_e \ln(m_0 / m_f). Explain what each symbol represents and why small increases in Δv\Delta v requirement (e.g. from LEO to the Moon) dramatically increase the initial mass m0m_0 for a fixed payload.
    2. A Mars-surface sample return mission has multiple spacecraft elements — orbiter, lander, ascent vehicle, sample capsule. Explain why this staged approach is preferred over a single monolithic design, referencing the rocket equation.
    3. Argue for or against sending humans (rather than robots) to Mars. Give one scientific, one economic and one ethical reason for your position.
    4. A near-Earth asteroid is discovered on a collision course with Earth, impact due in 2020 years. Describe, in general terms, how current space technology could deflect it, and why early warning is crucial.
Answers

Answer key

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Year 10 answers

Fluency

Telescopes

    1. No atmospheric blurring or absorption, so sharper images and access to wavelengths (X-ray, UV, infrared) that ground telescopes cannot detect.
    2. Earth’s atmosphere absorbs X-rays completely; they must be observed above it.
    3. Infrared.
    4. Pulsars, radio galaxies, cool dust clouds that hide star formation, and distant quasars. Radio also penetrates dust.
    5. Hubble Deep Field (distant galaxies); cosmic microwave background by WMAP and Planck; exoplanet atmospheres by Kepler and James Webb. (Any reasonable answer.)
Fluency

Rockets and orbits

    1. For every action there is an equal and opposite reaction. A rocket pushes hot exhaust gases backwards; the gases push the rocket forwards.
    2. 7.8\sim 7.8 km/s (about 2800028\,000 km/h).
    3. An orbit with a 2424-hour period so the satellite appears fixed above one spot on the equator; altitude is fixed by the requirement that orbital period equals one Earth day.
    4. Both the station and the astronauts are in continuous free-fall; no surface pushes up on the astronaut, so they feel weightless.
    5. Escape velocity is the minimum speed needed to leave Earth’s gravity altogether (11.2\sim 11.2 km/s). Orbital velocity only needs to keep an object in free-fall around Earth.
Fluency

Missions and applications

    1. Yuri Gagarin, 1961.
    2. 1960s to early 1970s (1969 - 1972).
    3. Weather: GOES, Himawari (any). Navigation: GPS (US), Galileo (Europe), GLONASS (Russia), BeiDou (China).
    4. USA (NASA, SpaceX), Russia (Roscosmos), China (CNSA). (Any two.)
Reasoning

Explain and justify

    1. Reaching orbital speed (~7.87.8 km/s) requires so much Δv\Delta v that most of the launch mass must be propellant; additionally, the fuel itself must be lifted up through the lower atmosphere, requiring yet more fuel.
    2. There is no air in space, so the engine must carry its own oxygen (or equivalent oxidiser) to burn the fuel.
    3. Each satellite gives only a sphere of possible positions. Three satellites intersect to two points; a fourth resolves ambiguity and corrects the receiver’s clock.
    4. Human radio transmissions (mobile phones, Wi-Fi, TV) are radio noise that swamps faint astronomical sources. Remote sites minimise interference.
    5. Mars: longer duration (~2-3 years), cosmic radiation outside Earth’s magnetic field, much bigger distance, communication delay of 20\sim 20 minutes each way, no rescue possible. Far greater risks than a few-day Moon mission.
Problem solving

Apply

    1. Distance from Earth’s centre: 6400+20200=266006\,400 + 20\,200 = 26\,600 km. Signal time =202003.0×1050.067= \dfrac{20\,200}{3.0 \times 10^5} \approx 0.067 s (from satellite to ground, approximate).
    2. Time =384000550069.8= \dfrac{384\,000}{5\,500} \approx 69.8 h 2.9\approx 2.9 days. (Real Apollo missions took about 3 days.)
    3. d=ct=3.0×105×0.12=36000d = ct = 3.0 \times 10^5 \times 0.12 = 36\,000 km. Matches the geostationary altitude.
    4. Mars and Earth move on different orbits; a minimum-energy (Hohmann) transfer is only possible when the two planets are in the right relative positions, which happens every 26\sim 26 months.
Reasoning

Challenge

    1. Δv\Delta v: required velocity change; vev_e: exhaust velocity; m0m_0: initial mass (with fuel); mfm_f: final mass (after fuel burn). The ratio m0/mfm_0/m_f grows exponentially with Δv\Delta v, so a modest increase in required Δv\Delta v multiplies the fuel (and initial mass) needed.
    2. Each stage can be optimised for its task and discarded when empty, reducing the mass that subsequent stages must accelerate. Monolithic designs carry the mass of empty tanks all the way, wasting fuel.
    3. Scientific: humans can adapt, improvise, and collect diverse samples faster than robots. Economic: robots cost orders of magnitude less and need no life support. Ethical: subjecting humans to unknown radiation and travel risks raises serious responsibility questions; arguments exist on both sides. (Any reasoned answer.)
    4. A kinetic impactor or gravity tractor could be sent to nudge the asteroid’s trajectory. Over many orbits, a tiny Δv\Delta v translates to a large miss distance; 2020 years of warning makes this feasible. Short warning would require much more energy and may be impossible.

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