What diameter telescope is needed to resolve the separation between an Earth-like planet and its star at 550 nm if the linear separation between them is 1 AU and the star system is 1 pc from Earth?

The NASA Kepler mission detected a transiting planet that blocks 1.3% of the stars light and the host star has a radius 82% of the  Sun's radius (the Sun has a radius of 700,000 km) what is the radius of the exosolar planet in km?

What would the angle between the Sun and the Earth be if the solar system were viewed from a distance of 1 pc?

A planet is detected at 0.5" from its star. The star is 10 parsecs away. How many AU from its star is the planet?

What diameter telescope is needed to see the separation between Uranus and its largest moon, Titania, from Earth at 550 nm, when Earth is 19.7 AU away? The moon is 436,300 km from the center of the planet. (Enter your answer in m.) m

Calculate the parallax angle for Mars located at 3400 km from Earth.

There are two parts to this question. I need to know how many times fainter Venus is from a distance of 6 pc and what the apparent magnitude would be as well! Thank you!!

A planet was recently discovered orbiting the star Proxima Centauri, with an orbital radius of 0.05 AU. As seen from Earth, what is the maximum angular separation between this planet and Proxima Centauri, in arcseconds? The distance to Proxima Centauri is 4.24 light-years.

Calculate how long radio communications from the spacecraft will take when it encounters Mars.  The furthest distance from Earth to Mars is 2.66 AU.  Remember that 1 AU = 1.5 x 1011 m and that light travels at 3 x 108 m/s.  So how long will the radio messages take to travel this greatest distance of 2.66 AU?           If two way communication between the Earth and the spacecraft involve a 1 s time lapse before an acknowledging signal is sent by the spacecraft, how long a time is there between sending a command to the spacecraft and receiving a reply?