Question

Many exoplanets have been discovered by the transit method, wherein one monitors a dip in the intensity of the parent star as the exoplanet moves in front of it. The exoplanet has a radius R and the parent star has radius $ 100\,R $ . If $ {I_ \circ } $ is the intensity observed on earth due to the parent star, then as the exoplanets transits.
(A) The minimum observed intensity of the parent star is $ 0.9\,{I_ \circ } $ .
(B) The minimum observed intensity of the parent star is $ 0.99\,{I_ \circ } $ .
(C) The minimum observed intensity of the parent star is $ 0.999\,{I_ \circ } $ .
(D) The minimum observed intensity of the parent star is $ 0.9999\,{I_ \circ } $ .

Answer 1

Hint :Let us first know about the exoplanets. Our solar system's planets all revolve around the Sun. Exoplanets are planets that orbit around other stars. Exoplanets are extremely difficult to see directly with telescopes. The dazzling glare of the stars they orbit obscures them. As a result, astronomers rely on alternative methods to detect and study these faraway planets. They look for exoplanets by observing their impacts on the stars around which they orbit.

Complete Step By Step Answer:
The transit method has been used to discover the majority of known exoplanets. When a planet passes between a star and its observer, it is called a transit. When Venus or Mercury pass between us and the Sun, transits inside our solar system can be seen from Earth. Transits reveal an exoplanet not because we can see it directly from many light-years away, but because the planet passes in front of its star, dimming its light significantly. This dimming can be seen in light curves, which are graphs that illustrate how much light is received over time. When the exoplanet passes in front of the star, the light curve will show a dip in brightness. The size of the planet itself can be calculated based on how much the star’s brightness is lowered.
Minimum observed intensity is given by:
 $ I = {I_ \circ } - \dfrac{{{A_p}}}{{{A_s}}}{I_ \circ } $
Where, $ {A_p} = $ effective area of planet
 $ {A_s} = $ Effective area of star
 $ I = {I_ \circ }\left[ {1 - \dfrac{{{R^2}}}{{{{(100R)}^2}}}} \right] $
 $ I = {I_ \circ }\left[ {\dfrac{{9999}}{{10000}}} \right] $
 $ I = 0.9999{I_ \circ } $
So, the option (D) is correct.

Note :
During a transit, we can also learn about an exoplanet's atmosphere. Some light will pass through its atmosphere as it transits, and this light may be studied to see what atmospheric factors impacted its unique dispersion. The composition of the atmosphere is crucial in determining habitability. Habitability can also be determined by the size of the orbit and the temperature of the star. These assist in determining the temperature of the planet itself, indicating whether its surface is suitable for life or not.