Week 38 – How long does light from the Sun take to reach Earth?

Our live are largely built around the rising and setting of the Sun in the sky each day.  Our biology is intimately connected to this via our circadian rhythms:

Have you ever wondered what would happen if the Sun just suddenly blinked out of existence?  When would you know?  Turns out, it takes time for light to travel from the Sun to the Earth.  We’ve just learned that light travels at a constant speed, c, in a vacuum like outer space.  We know that c = 3.0 x 108 m/s.  To calculate how long it takes light to travel from the Sun to Earth, we need to know the distance between the two.  While the orbit of Earth around the Sun is not a perfect circle, on average the Earth is about 93 million miles (mi) from the Sun.  Time for some math!

Have: c = 3.0 x 108 m/s and distance = 93 x 106 mi

Want: Time it takes light to travel from the Sun to Earth

Need: Connection between meters (m) and miles (mi)

Another quick Google search tells us there are 1609.34 meters in 1 mile.  We are in business!

Calculation: (93 x 106 mi) x (1609.34 m / 1 mi) x (1 s / 3.0 x 108 m) = 499 s

Analysis: It takes about 499 seconds for light to travel from the Sun to the Earth!  Divide 499 by 60 and that gives us about 8.3 minutes.  So if the Sun blinked out right now, at this very instant, we wouldn’t know until 8.3 minutes from now.  The Sun is our nearest star, and it still takes 8.3 light-minutes for its light to reach us.

The second closest star to Earth is called Alpha Centauri.  Alpha Centauri is actually a triple star system (three stars in orbit around each other) located approximately 4.37 light-years from Earth.  Traveling at the speed of light, c, it would take 4.37 years to reach Alpha Centauri.  How many miles away is that?

4.37 light-years x (365 days / 1 year) x (24 hours / 1 day) x (60 minutes / 1 hour) x (60 seconds / 1 minute) x (3.0 x 108 meters / second) x (1 mile / 1609.34 meters) = 2.57 x 1013 miles, or 25.7 trillion miles away!

That’s a long way!  It also means that if you look at Alpha Centauri in a telescope (or just look in the right part of the night sky), you are actually seeing light that left the star system 4.37 years ago.  You are literally looking back in time!  In fact, every time you look up in the night sky, you are looking back in time.

If traveling 4.37 years at the speed of light seems like a long time, don’t despair.  The distance from Earth to the nearest planet outside our solar system is a bit less.  Discovered in 2016, the planet Proxima Centauri b orbits Alpha Centauri and is “only” about 4.2 light-years from Earth.

Last week, MIT Technology Review announced the likely discovery of an Earth-like planet around a Sun-like star. (To be more accurate, and to give you a sense of how the scientific process works, the exoplanet was observed, the findings were written up into a scientific article and submitted to the scientific journal Astronomy & Astrophysics on October 16, 2019, and after successfully completing the peer-review process, the article was accepted for publication on May 3, 2020 and then published by the journal on June 4, 2020.  Here is the link to the published article.)  The exoplanet is named KOI-456.04 and is 3,140 light-years from Earth.  

While humanity hasn’t yet engineered a solution for how to accelerate a large spacecraft to near the speed of light, the video below introduces some important concepts regarding near light-speed travel.

Finally, if you think a bit more about the idea that looking at the stars is like looking back in time, the same hold true for Earth.  An alien pointing a telescope at Earth would be looking back in time at Earth as it was when the light left Earth.  If the alien is currently 65 million light-years from Earth, then the light they are observing today through their telescope left Earth 65 million years ago.  Is there a sufficiently powerful telescope that would allow the alien to actually see dinosaurs on Earth?  So glad you asked!

Return to Week 38 – Properties of Light and continue working.

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