## Friday, June 14, 2013

### How far can the Sun be seen?

How far away from the Sun can you just barely see the Sun (using Wikipedia)? The Sun is magnitude -26.74 (from Wikipedia). The dimmest stars one can see with the naked eye are approximately magnitude 6. The Sun would have to be |-26.74 - (6)| = 32.76 magnitudes dimmer. The formula for magnitudes is x^5 = 100, x = 100^(1/5), where x is the multiplier to get from one magnitude to the next. The factor dimmer that Sun must be is x^32.76=12,705,741,052,085 (more or less). Light gets dimmer with the square of the distance. Since the Sun is at one AU (x^32.76)^(1/2)=3,564,511 AU is the distance where you can just barely see the Sun. How far is that? 1 AU = 149,597,870,700 meters, exactly. 3,564,511 AU * 149,597,870,700 m/AU = 533,243,305,691,677,319 meters. 1 light-year = 9460730472580800 metres (exactly). 533,243,305,691,677,319 m / 9.4607×10^15 m/LY = 56.363861885414590497131460401964 light years. (OK, so that's more digits than we need). If you were 56.364 Light Years away, you'd be just barely able to see the Sun.