Question

The diameter of the Sun is 1.39 million kilometres and the Earth is 8.3 light minutes far away.
Proxima Centauri is the nearest star - it has a distance of 4.24 light years to our Sun.
(a) How long does it take to travel to Proxima Centauri with
(i) an airplane (920 km/h) or
(ii) with the Voyager 1 space probe (17 km/s).
(b) Let the Sun have the size of a tennis ball (diameter: 6.7 cm): How far away is the Earth and
how far away is Proxima Centauri on this scale?

Answer 1

a) i)

$$t= \frac{(4.24)9.46 \cdot 10^{12}}{920}=4.4\cdot 10^{10} \ h$$

ii)

$$t'= \frac{(4.24)9.46 \cdot 10^{12}}{17}=2.4\cdot 10^{12} \ s$$

b)

$$D_E=(8.3) 1.8\cdot 10^{7} \frac{6.7}{1.39 \cdot 10^{6}}=720\ cm= 7.2 \ m$$

$$D_{PC}=(4.24)9.46 \cdot 10^{12} \frac{6.7}{1.39 \cdot 10^{6}}=1.9 \cdot 10^{8}\ cm= 1900 \ km$$