10. Astronomers use astronomical units (AU) to describe distances in our solar system. The distance between the Sun and the Earth is 1 AU. 1 AU is 1·496 × 108 km, correct to 4 significant figures.
(a) The distance of Pluto from the Sun is 5·913 × 109 km, correct to 4 significant figures.
Diagram not drawn to scale
Siôn says that the distance of Pluto from the Sun is less than 50 AU.
Using suitable approximations, estimate the distance of Pluto from the Sun, in AU, to show that Siôn is correct. You must show all your working. [2]
(b)
A light year is the distance light travels in one year.
1 light year is approximately 63 000 AU.
Estimate the length of a light year in km. Give your answer in standard form. [3]
Mark scheme (a)
Scheme
Marks
Comments
\(\dfrac{6 \times 10^{9}}{1{\cdot}5 \times 10^{8}}\) or equivalent
M1
A calculation, using approximations, that would lead to an answer of < 50
40 or 4 × 101
A1
FT their calculation e.g. \(\dfrac{5{\cdot}9 \times 10^{9}}{1{\cdot}5 \times 10^{8}}\) leads to an answer of 39·33
Mark scheme (b)
Scheme
Marks
Comments
63000 × 1·5 × 108 OR 60000 × 1·496 × 108 OR 60000 × 1·5 × 108
M2
Acceptable options for M2 and A1 Award M1 only for 63000 × 1·496 × 108 Or M1 for 1 slip in the power of 10, but otherwise correct
= 9·4(5) × 1012 (km) OR 8·9(76) × 1012 (km) OR 9 × 1012 (km)
A1
FT from M2 only If no marks awarded, SC1 for 6(·3) × 1012 (km)
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