Forces and Motion

Equation

time = distance——————velocity

t =  dv

1.2

Light year

Light year = distance light travels in a year

= 9.46 • 1012km

Speed and Velocity

Now Try This!

The nearest bright star beyond our sun is called Alpha Centauri. It is easily visible in the night sky if you live on Earth’s southern hemisphere. Alpha Centauri is orbited by a planet, the nearest one beyond our solar system.

Alpha Centauri is 4.37 light years away. That doesn’t sound too far until you remember that one light year = the distance light travels in a year which is about 10 trillion kilometers! So, Alpha Centauri is about 44 trillion kilometers away (give or take a few billion). How long would it take to travel to Alpha Centauri flying in the Space Shuttle going 28,000 kilometers per hour?

Left: Alpha Centauri: The nearest bright star beyond our sun at 4.37 light years away. Photo from ESO/Digitized Sky Survey 2.

Remember v = d/t? Rearrange that equation to find t:

time =distance——————velocity t =  dv

The distance of 44 trillion kilometers is too big to write out so we use scientific notation. As the Appendix shows a trillion is 1012 so

44 trillion km = 44 x 1012 km

but remember in scientific notation there is only one digit before the decimal so the distance, d, is 4.4 x 1013 km

And converting the velocity of 28,000 km/hr to scientific notation requires putting a decimal point after the 2 and counting over 4 spaces to the rightmost digit.

28,000 km/hr = 2.8 x 104 km/hr

Now we are ready to do the problem!

t = 4.4 x 1013 km/2.8 x 104 km/hr = 1.6 x 109 hr

and since there are 24 hrs/day x 365 days/yr = 8,760 = 8.76 x 103 hrs in a year,

1.6 x 109 hr / 8.76 x 103 hr/yr  = 1.8 x 105 = 180,000 years to reach the star!

Clearly, a faster vehicle is required if humans are ever going to travel to the stars!

Yes or No?

So, should NASA send astronauts to Alpha Centauri using present technology? Yes or No?

Yes
No

No. Human space travel to stars requires a warp drive from science fiction. Otherwise, the immense distances between stars means that any rockets we have today would take far longer than not just the human lifespan, but the entire span of human evolution.

Can you solve this?

If you could travel at the speed of light (300,000 km per second), how long would it take you? (Hint: no, calculation is necessary if you remember the definition of a light year).