As mentioned before, our asteroid is in the shape of a sphere and has a mass of 1000 kilograms. determine the density (in grams per cubic centimeter) of this asteroid if its diameter is known to be 1.2 meters. useful information: 1 kg = 1000 g, 1 m = 100 cm, volume of sphere = 4/3 ? r3. remember that the radius of a sphere is equal to half its diameter. show all of your work. (20 points)

Explanation:

Density is a characteristic property of a material and is defined as the relationship between the mass and volume of a specific substance or material. So, the density of the asteroid is given by the following equation:

  (1)

On the other hand, we know the asteroid has a mass and is spherical. This means its volume is given by the following formula:

  (2)

Where  is the radius of the sphere and is half its diameter .

Knowing this, we can calculate the volume:

  (3)

  (4)

Substituting (4) in (1):

  (5) This is the density of the asteroid, but we were asked to find it in . This means we have to make the conversion:

Finally:

explanation:

the masses of the objects and the distance between them