Considering both the distance between Earth and the Sun and the speed of light, how long would it take a radio wave from Earth to reach the nearest star?

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belarafon | High School Teacher | (Level 2) Educator Emeritus

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Throughout the history of astronomy, several stars have been labeled "closest" to the Solar System based on various types of science. For years, the binary star Alpha Centauri was thought to be closest, with a distance of about 4.37 lightyears. However, more recent findings have discovered that Proxima Centauri, a star close to Alpha Centauri ("proximate") is actually closer, with a distance of about 4.24 lightyears. Given this distance, the time it would take a radio wave to reach Proxima Centauri is easy to calculate.

The speed of light is approximately 299,792.5 km/s, which makes the distance of one lightyear about 9.4605284 × 10^12 (about 10 trillion km, the distance light travels in one year in a vacuum). If Proxima Centauri is 4.24 lightyears from the Earth, it is about 42.4 trillion km away; radio waves travel at the speed of light in a vacuum, so it would take a radio wave from Earth about 141,431,156.5 seconds to reach Proxima Centauri, and the same amount of time for a radio wave to return. Dividing that number into minutes, hours, etc., the final number is about 58 months, or almost five years. That means that a radio wave from Earth would take almost five years to reach Proxima Centauri, and another five years (give or take alien response time) for a reply.

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