Final answer:
The length of the comet's tail, when observed at an angle of 1.1 degrees from Earth located 0.69 AU away, is approximately 0.013248 AU.
Step-by-step explanation:
To calculate the length of the comet's tail in astronomical units (AU), we need to use the fact that the comet's tail forms an arc that subtends an angle of 1.1 degrees at the observer's eye. To find the length of the arc (tail of the comet), we can use the formula:
L = θ × r
where L is the arc length, θ (theta) is the angle in radians, and r is the radius of the circular arc. The angle must be in radians for the calculation, which we find using this conversion:
θ = (°/360) × 2π = (1.1°/360°) × 2π = 0.0192 radians.
Because the comet is 0.69 AU from Earth, this will be the radius r that we use in our calculation:
L = 0.0192 × 0.69 AU = 0.013248 AU
Therefore, the length of the comet's tail is approximately 0.013248 AU.