Final answer:
To see the Sun and Jupiter as distinct points of light from a distance of 10 light years, you would need an angular resolution calculated using the small-angle formula. This formula takes into account the size of the objects and the distance to the objects. By converting the given values of the apparent orbit diameters of Jupiter and the Sun to degrees and applying the small-angle formula, the angular resolution can be calculated.
Step-by-step explanation:
To calculate the angular resolution needed to see the Sun and Jupiter as distinct points of light from a distance of 10 light years, we can use the small-angle formula. The diameter of Jupiter's apparent orbit viewed from Alpha Centauri is given as 10 seconds of arc, and the diameter of the Sun's orbit is 0.010 seconds of arc. We can convert these values to degrees and then apply the small-angle formula to find the angular resolution.
First, we convert 10 seconds of arc to degrees by dividing by 3600, which gives us 0.002778 degrees. Similarly, 0.010 seconds of arc is equivalent to 0.00000278 degrees.
The small-angle formula states that the angular resolution is equal to the size of the object divided by the distance to the object. In this case, we want to find the angular resolution needed to see the Sun and Jupiter as separate points of light, so the size of the objects is the diameter of their apparent orbits. The distance is given as 10 light years, which is equivalent to 10 * 9.461 × 10^15 meters.
Using the small-angle formula, we have:
Angular resolution = (size of object) / (distance) = (0.002778 + 0.00000278) degrees / (10 * 9.461 × 10^15 meters)
Calculating this expression gives us the angular resolution needed to see the Sun and Jupiter as distinct points of light from a distance of 10 light years.