How Far Away the Sun Is?
Simple - ish. You can use simple triangle geometry. Consider this drawing of the moon at first quarter when half the moon is lit on the side toward the sun.
In ancient Greece a guy named Aristarchus was the first to at least show that the sun was MUCH farther away than the moon. Before this the things moved in the sky against a backdrop of the starry sky more or less together like things on a movie screen. By measuring at first quarter he reasons that the angle between the earth - moon and moon-sun is a right angle. Aristarchus thinks that if he could measure the angle between the moon and the sun at first quarter he could at least know if the sun was about as far away as the moon, closer than the moon or farther away than the moon. A big angle would mean the sun was far while a small angle would mean the sun was close. And by the way, this is typical in the history of knowing stuff. You start with a pretty good approximation based on known math or science. Others then pick up on this and improve on your idea, improve on your measurement.
In Aristarchus’ case this was a very tough measurement. Has to be made exactly when the moon is at first quarter so that the angle between earth-moon and moon sun is 90 degrees. Also he’s using pretty crude measuring devices. Still he measured an angle of around 87 degrees showing that the sun was much farther away than the moon - about 19 times farther way based on this calculation1 While this is not so close to the actual number, he was successful in showing that the sun is way out there.
In general this method is called measuring by parallax. Once you have a baseline (in this case earth-moon distance) and a couple of angles you can find the unknown distance. This is simple surveying as done on earth to lay out property lines. The great distances and tiny angle variation for celestial measurements presents a challenge but no new math is involved.
This is also a good example for us to have some understanding that there is a way to know something without doing the calculation ourselves. You can, hopefully, see that knowing one thing leads to another using known methods.
In ancient Greece a guy named Aristarchus was the first to at least show that the sun was MUCH farther away than the moon. Before this the things moved in the sky against a backdrop of the starry sky more or less together like things on a movie screen. By measuring at first quarter he reasons that the angle between the earth - moon and moon-sun is a right angle. Aristarchus thinks that if he could measure the angle between the moon and the sun at first quarter he could at least know if the sun was about as far away as the moon, closer than the moon or farther away than the moon. A big angle would mean the sun was far while a small angle would mean the sun was close. And by the way, this is typical in the history of knowing stuff. You start with a pretty good approximation based on known math or science. Others then pick up on this and improve on your idea, improve on your measurement.
In Aristarchus’ case this was a very tough measurement. Has to be made exactly when the moon is at first quarter so that the angle between earth-moon and moon sun is 90 degrees. Also he’s using pretty crude measuring devices. Still he measured an angle of around 87 degrees showing that the sun was much farther away than the moon - about 19 times farther way based on this calculation1 While this is not so close to the actual number, he was successful in showing that the sun is way out there.
In general this method is called measuring by parallax. Once you have a baseline (in this case earth-moon distance) and a couple of angles you can find the unknown distance. This is simple surveying as done on earth to lay out property lines. The great distances and tiny angle variation for celestial measurements presents a challenge but no new math is involved.
This is also a good example for us to have some understanding that there is a way to know something without doing the calculation ourselves. You can, hopefully, see that knowing one thing leads to another using known methods.
Comments
Post a Comment