FAQ/Sun: Difference between revisions

Using trigonometric identities and Taylor series approximations, to a large number of significant figures we have that sin(θ<small>2</small>) = 0.9999999*sqrt(2)/2. Since sin(45deg) = sqrt(2)/2, we have that n<small>2</small> = 1/0.9999999 = 1.000 000 1 to good approximation. Most gas in outer space is said to be hydrogen, which has a lower index of refraction than air at similar pressure and temperature, thus, if we use the Ciddor equation to estimate the gas density needed for n<small>2</small>, hydrogen gas will require a higher density to achieve the same index of refraction. For example, if we calculate (ignoring the scale of the numbers) using Ciddor that our outer space gas patch requires a density of 0.5atm to bend the light by the given angle, we will actually require a larger density such as 0.6atm. To get in the ballpark of the actual numbers, we can use the Ciddor equation, but we are well outside of the usual values of the input variables, making the Ciddor formula less reliable for our purposes. We get the equation y = (3.37615288E-06)*x+0.99999992 for a trendline when fixing the temperature at -40degC and the relative humidity at 0, and letting x, the pressure in kPa vary, where y is the index of refraction. If y = 1.000 000 1, then the pressure is 0.0533151241658kPa. As mentioned, for hydrogen gas, this would be higher, but this is a ballpark calculation, so we will not alter the required pressure. The pressure in outer space is said to be 1.322E-11 Pa, or 1.322E-14 kPa. We will just look at orders of magnitude. We needed a pocket of gas in space with a pressure of about 1E-2 kPa of pressure, but outer space is said to have a pressure of 1E-14 kPa, which is 10^12, or a trillion times smaller than it needs to be. This all assumes that just one pocket of gas in space causes the light to refract, and likely, a light ray would encounter multiple pockets of gas if any, however, the new direction for the light ray would likely be random,. makingA itrandom difficultwalk forwill theneed lightto raybe defined and studied to accumulatedetermine anyhow significanta changeray inwill directionrefract asthrough itouter travelledspace. In summary, it seems unlikely for a light ray to encounter a dense enough patch of interstellar gas to cause a 0.000 000 1deg change in direction. More work will need to be done to determine if Snell's law predicts that the stars' light will miss us.