answer each of the following with a brief explanation of the mathematics used to get there. A new mystery planet is detected around our Sun. We measure its position relative to the Sun to be 2 AU at perihelion and 6 AU at aphelion. What is the semimajor axis of this planet's orbit (in AU)? With that information, what is the orbital period of that planet (in years)? If this planet has the same mass as Earth, how does the average force of gravity on the planet by the Sun compare with the average force of gravity on the Earth by the Sun? Please give a numerical ratio of the forces. (Hint: You can take the semimajor axis to represent the average position of the planets)

answer each of the following with a brief explanation of the mathematics used to get there. A new mystery planet is detected around our Sun. We measure its position relative to the Sun to be 2 AU at perihelion and 6 AU at aphelion. What is the semimajor axis of this planet's orbit (in AU)? With that information, what is the orbital period of that planet (in years)? If this planet has the same mass as Earth, how does the average force of gravity on the planet by the Sun compare with the average force of gravity on the Earth by the Sun? Please give a numerical ratio of the forces. (Hint: You can take the semimajor axis to represent the average position of the planets)