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Calculations: Please show your work which means, write out the equation, show the steps and final answer including units.

1. We discussed Kepler's third law in class and how the planet-Sun distance is related to the orbital period (time it takes for the planet to circle around the Sun once). The orbital period is measured in Earth years and distance is measured in AU (astronomical units) which is the Earth-Sun distnce. Using Kepler's third law, answer the following questions.

   a) What is the orbital period of an object at distance of 4 AU from the Sun?

   b) What is the orbital period of an abject at a distance of 100 AU from the Sun?

   c) What is the distance to an object which has an orbital period of 36 years?

2. Density is an important characteristic that planetary astronomers use to determine the composition of a planet. Density is usually measured in grams per cubic centimeter.

   The following guideline shows the general composition of the object based on the density.

   rocky with a core: (Density > 5g/cc)
   rocky: (3 g/cc < Density < 5 g/cc)
   rock and ice: (1.5 g/cc < Density < 3 g/cc)
   icy: (1 g/cc < Density < 1.5 g/cc)
   mostly gas: (Density <1g/cc)

   The Earth's bulk (average) density is 5.5g/cc meaning that it is rocky with an iron/nickel core. Please calculate the following densities and using the above guideline, state the general composition of the object. The values are given in terms of Earth mass (6 x 10^27 g) and Earth radius (6.37 x 10^8 cm) so that you can use the density of the Earth to calculate the new densities. See Lecture 2 under week 3, there are several examples of this. If this is confusing, use the above values of Earth mass and radius to find the numbers and calculate the density from these.

   a) mass = 1/5 of Earth mass; radius = same as Earth Radius

   b) mass= 3 times Earth mass; radius = 2 times Earth radius

   c) mass= 1/8 of Earth mass; radius = 1/2 times Earth radius

   d) mass= 10 times Earth mass; radius = 5 times Earth radius

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3. NASA recently received results from a satellite/mission called LCROSS. Google it and tell me what the objectives were and what it found.

4. Dawn is another satellite mission from NASA launched almost 3 years ago. Summarize the science goals of Dawn.

5. How do crater counts on the surfaces of objects in our solar system help to determine the age of that surface? How do we know that there were two distinct cratering epochs on the Moon?