Space Physics — Numerical Practice
Covers: orbital speed (v = 2πr/T), light travel time and light-years, and the Hubble constant (H₀ = v/d, d/v = 1/H₀). 16 questions.
A. Orbital Speed
A satellite orbits Earth at an average radius of 7 × 10⁶ m, with an orbital period of 5800 s. Calculate its orbital speed.
A moon orbits a planet at a radius of 4 × 10⁵ m with a period of 7.2 × 10⁴ s. Calculate its orbital speed.
A planet orbits a star with a period of 3.15 × 10⁷ s at an average radius of 1.5 × 10¹¹ m. Calculate its orbital speed.
A satellite has an orbital speed of 3000 m/s at a radius of 8 × 10⁶ m. Calculate its orbital period.
Explain why a planet further from the Sun has a slower orbital speed than a planet closer to the Sun.
B. Light Travel Time and Light-Years
The distance from the Earth to the Sun is approximately 1.5 × 10¹¹ m. Calculate the time light takes to travel this distance. (speed of light = 3 × 10⁸ m/s)
A star is 4 × 10¹⁶ m away. Calculate the light travel time in seconds, then convert this to years (1 year ≈ 3.15 × 10⁷ s).
A star is 6.5 light-years from Earth. Calculate this distance in metres. (1 light-year = 9.5 × 10¹⁵ m)
Convert a distance of 2 × 10¹⁷ m into light-years.
The Moon is 3.84 × 10⁸ m from Earth. Calculate the time light takes to travel this distance.
Explain why astronomers use light-years rather than metres to state distances to stars.
C. The Hubble Constant and the Expanding Universe
A galaxy recedes from Earth at 5 × 10⁶ m/s. Using H₀ = 2.2 × 10⁻¹⁸ /s, calculate its distance from Earth.
A galaxy is 3 × 10²⁴ m from Earth. Using H₀ = 2.2 × 10⁻¹⁸ /s, calculate its recession speed.
Using H₀ = 2.2 × 10⁻¹⁸ /s, estimate the age of the Universe in seconds, then convert this to years (1 year ≈ 3.15 × 10⁷ s).
Explain what redshift is, and how it provides evidence for an expanding Universe.
Explain why the equation d/v = 1/H₀ giving the same value for many different galaxies supports the Big Bang theory.
Mastery Test
A satellite orbits at a radius of 5 × 10⁶ m with a period of 4500 s. Calculate its orbital speed.
A distance of 9 × 10¹⁰ m is crossed by light. Calculate the time taken. (speed of light = 3 × 10⁸ m/s)
Convert a distance of 3 light-years into metres. (1 light-year = 9.5 × 10¹⁵ m)
Convert a distance of 1.9 × 10¹⁶ m into light-years.
A galaxy recedes at 8.8 × 10⁶ m/s. Using H₀ = 2.2 × 10⁻¹⁸ /s, calculate its distance.
A galaxy is 5 × 10²⁴ m away. Using H₀ = 2.2 × 10⁻¹⁸ /s, calculate its recession speed.
Explain, using the Sun’s gravitational field, why more distant galaxies and planets tend to have slower orbital/recession relationships than closer ones (in the case of planets, slower orbital speed).
Explain what evidence the cosmic microwave background radiation (CMBR) provides for the Big Bang theory.
State the approximate diameter of the Milky Way galaxy, in light-years.
Explain why light from the Sun takes a measurable amount of time (about 8 minutes) to reach the Earth.
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