Question

Light from the star Betelgeuse takes about 400 years to reach the Earth.There are about 3.1×10⁷ seconds in a year and the speed of light is about 3.0×10⁸ m/s.(i) Show that the distance of Betelgeuse from Earth is about 4×10¹⁸ m [I have done this part, this is only here for context].In January 2006, the spacecraft New Horizons was successfully launched, travelling at about 25000 m/s to Pluto, and should arrive in 2015.(ii) Assuming that the spacecraft carries on towards Betelgeuse at the same speed, calculate the time, in years, that it would take to reach Betelgeuse.(iii) Suggest and explain whether, with our current technology, human travel between stars is possible.

Answer 1

Given that the distance of Earth from Betelgeuse is

$d=\text{ }4\times10^{18}\text{ m}$

There are 3.1 x 10^7 s in a year.

(ii) Also, the speed is v = 25000 m/s

The time taken in seconds will be

$\begin{gathered} v=\frac{d}{t} \\ t=\frac{d}{v} \\ =\text{ }\frac{4\times10^{18}}{25000} \\ =1.6\times10^{14}\text{ s} \end{gathered}$

The time taken in years will be

$\frac{1.6\times10^{14}}{3.1\times10^7}=5.1\times10^6years_{}$

(iii) The distance between stars is very huge, so the time taken to travel that much distance is very large.

It might take a lifetime of humans with the current existing technology.

To increase the speed and decrease the time for traveling, a lot of fuel and energy will be required which is not possible with current resources and technology.

Thus, with our current technology, human travel between stars is not possible.