The largest known star (until June 2019) is VY Canis Majoris in the constellation of Canis Major with an estimated
diameter of 1,975,000,000 km. Making the (absurd) assumption that a commercial jet could fly close to the surface of
the star at a constant speed of 990 km / h, how long would the jet take for a spin on the star, answer in years.
Problem data
- star diameter: D = 1,975,000,000 km;
- jet speed: v = 990 km/h.
Problem diagram
Solution
The distance that the airplane should travel is the circumference of the star, the length of a circle is given by
\[
C=2\pi r
\]
where
r is the radius of the circumference, the diameter of a circle being equal to 2
r, the length of a
circle can also be calculated by
\[
C=\pi D
\]
where π = 3,14 the circumference of the star is
\[
C=3.14 \times 1975000000\\
C=6201500000\;\text{km}
\]
As the plane speed is constant, we have that travel time is given by
\[
v=\frac{\Delta S}{\Delta t}\\
\Delta t=\frac{\Delta S}{v}
\]
using the speed value given in the problem and the distance being the length of the circumference calculated above,
we have
\[
\Delta t=\frac{6201500000}{990}\\
\Delta t=6264141\;\text{h}
\]
Converting this value to years as it asks for the problem, we get
\[
\Delta t=6264141\;\cancel{\text{hours}} \times \frac{1\;\cancel{\text{day}}}{24\;\cancel{\text{hours}}} \times \frac{1\;\text {year}}{365\;\cancel{\text{days}}}
\]
\[ \bbox[#FFCCCC,10px]
{\Delta t=715\;\text{years}}
\]
Note: for comparison, the Sun is 1,391,000 km in diameter, under the same conditions, the airplane
would take "only" 184 days to go around the Sun.