Using the best telescopes under the best observing conditions, the smallest angle in the sky that can be resolved from Earth's surface is approximately 0.1 arcsec. (You may wish to review the small-angle formula in Box 1-1 of Universe, 11th ed.) Consequently, the smallest feature that can be resolved at the distance of Uranus is about:
A)1/400 of the diameter of Uranus.
B)1/4 of the diameter of Uranus.
C)4 times the diameter of Uranus.
D)1/40 of the diameter of Uranus.

Question

Quizplus · Accepted Answer

The smallest angle that can be resolved from Earth's surface is approximately 0.1 arcsec. Using the small-angle formula, we can calculate the distance that corresponds to this angle for Uranus:

0.1 arcsec = (diameter of Uranus) / distance

Solving for distance gives:

distance = (diameter of Uranus) / 0.1 arcsec

Using the diameter of Uranus (51,118 km), we get:

distance = 511,180 km

This is approximately 1/40 of the distance from Earth to the Moon. Therefore, the smallest feature that can be resolved on Uranus is about 1/40 of its diameter, or approximately 1,278 km.

Using the Best Telescopes Under the Best Observing Conditions, the Smallest