Detecting an Earth-like planet is a significant challenge due to the fact that it is approximately 10 billion times fainter than its parent star. The key obstacle lies in the need to block almost all of the star’s light in order to capture the faint light reflected from the planet. This requires the use of a coronagraph, which blocks starlight by exploiting differences in brightness between the star and its surrounding space. However, any instability in the telescope’s optics, such as misalignment between mirrors or a change in the mirror’s shape, can lead to leakage of starlight and cause glare that masks the planet.

To overcome these challenges and detect an Earth-like planet using a coronagraph, it is necessary to achieve exceptional control over both the telescope and the instrument’s optical quality. This requires precise calibration of every component in the system, from mirrors to sensors, to ensure that they are aligned perfectly and functioning optimally. In addition, advanced image processing algorithms must be used to separate out any background noise or interference that may be present in the captured images.

The level of precision required for this endeavor is truly remarkable. To achieve this level of accuracy, scientists must have control over every aspect of their instruments down to individual atoms. For example, if a hydrogen atom were placed at one end of a ruler 10 meters long, it would take 100 seconds for it to move one picometer (or 1×10^-12 meters). This means that any deviation from perfect alignment or optical quality could result in significant errors or even complete failure of the detection process.

In conclusion, detecting an Earth-like planet using a coronagraph presents many challenges due to its faintness compared to its parent star. However, with careful calibration and precise control over both telescope and instrumentation, scientists can overcome these obstacles and make groundbreaking discoveries about our universe’s potential habitats beyond Earth.