Final answer:
The 40-inch telescope has four times the light-gathering power of the 20-inch due to its larger aperture area. Space telescopes like the Hubble overcome atmospheric issues and aid in distance measurements through methods like parallax and redshift, integral to the cosmic distance ladder.
Step-by-step explanation:
When comparing the light-gathering power of telescopes, one with a 40-inch primary lens has significantly greater capabilities than a telescope with a 20-inch lens. The light-gathering power is directly proportional to the area of the lens or mirror, which means that the larger the aperture, the more light the telescope can collect. Given that the area is πr2, a 40-inch telescope has four times the light-gathering power of a 20-inch telescope, as the radius is doubled.
Space telescopes are pivotal across the electromagnetic spectrum due to their ability to bypass atmospheric distortion and collect data free from Earth's atmospheric interference. The Hubble Space Telescope, for instance, has been instrumental in the astronomical community because of its high-resolution capabilities.
One way telescope data can assist astronomers in determining distances between celestial objects is through methods like parallax and redshift. The cosmic distance ladder involves various rungs such as standard candles (like Cepheid variables) and redshift measurements of distant galaxies to calibrate and measure distances in the universe.