Question

Problem B.2: Distance of the Planets (6 Points) The table below lists the average distance R to the Sun and orbital period T of the first planets:
Distance Orbital Period
Mercury 0.39 AU 88 days
Venus 0.72 AU 225 days
Earth 1.00 AU 365 days
Mars 1.52 AU 687 days
(a) Calculate the average distance of Mercury, Venus and Mars to the Earth. Which one of these planets is the closest to Earth on average? (b) Calculate the average distance of Mercury, Venus and Earth to Mars. Which one of these planets is the closest to Mars on average? (c) What do you expect for the other planets? Hint: Assume circular orbits and use symmetries to make the distance calculation easier. You can approximate the average distance by using four well-chosen points on the planet’s orbit. PLEASE ANSWER ONLY IF YOU KNOW THE ANSWER CORRECTLY, OTHERWISE DON'T....

Answer 1

Answer: (A)Distance of mercury to the earth = 1.00AU-.39AU=.61AU

DISTANCE OF VENUS TO EARTH=1.00AU-.72AU=.28AU

DISTANCE OF MARS TO EARTH=1.52AU-1.00AU=.52AU

SO FROM THE RESULTS VENUS IS CLOSE TO THE EARTH

(B)DISTANCE MERCURY TO MARS=1.52AU-.39AU=1.13AU

DISTANCE MERCURY TO VENUS =1.52AU-.72AU=.8AU

DISTANCE MERCURY TO EARTH =1.52AU-1.00AU=.52AU

SO FROM THE RESULTS EARTH IS CLOSE TO MARS.

(C) AS THE DISTANCE FROM THE SUN INCREASES, GRAVITATIONAL FORCE DECREASES, VELOCITY DECREASES, SO THE ORBITAL PERIOD INCREASES

Explanation:

1 AU = 150 MILLION KM (which is measured from Sun to Earth)