Suppose there existed a planet that went around the sun twice as fast as the earth. What would by its orbital size?

Explanation

To solve the problem of finding the orbital size of a planet that orbits the sun twice as fast as the Earth, we can follow these steps:

### Step 1: Understand the relationship between time period and orbital radius
According to Kepler's Third Law of Planetary Motion, the square of the time period (T) of a planet is directly proportional to the cube of the semi-major axis (r) of its orbit. Mathematically, this can be expressed as:
\[ T^2 \propto r^3 \]

### Step 2: Define the known values
Let:
...