Can someone explain this because I dont understand the solutions
Thanks
Hello! The question is asking how it is possible for a telescope to have the same orbital period than the Earth's.
From Kepler's laws of periods, it gives us a ratio as shown:

Given that this is a RATIO, when one variable changes, the other variable HAS to change to keep the equation true, which is shown in the question. We know that the telescope has a larger radius than Earth's so theoretically, it should have a LARGER period.
However, the question states that they both have the same orbital period, which contradicts Kepler's law, and this is because Kepler's law only applies to TWO objects, and doesn't take into account other forces.
For Earth, It has all of its force coming from the sun, HOWEVER, the telescope has forces from BOTH the sun AND the earth, meaning the telescope is experiencing more FORCE than Earth's. As force is equal to the centripetal force, it has a HIGHER orbital velocity.
Hope this helps