Answer the following questions.

1- Suppose a dwarf planet is discovered orbiting the Sun with a semimajor axis of 50AU.

What would be the planet's orbital period?

2- Suppose you read online that "experts have discovered a new planet with a distance from the Sun of 2 AU and a period of 3 years." Use Kepler's third law to argue that this is impossible.

3- If a 100-kg astronaut pushes on a 5,000-kg satellite and the satellite accelerates at 0.1 m/s², what acceleration does the astronaut experience in the other direction?

4- At the surface of Earth, the escape velocity is 11.2 km/s. What would be the escape velocity at the surface of a very small asteroid having a radius 10^-4 that of Earth and a mass 10^-12 that of Earth?