Determining the density of a stellar object

Johnboy

1. The problem statement, all variables and given/known data
Hello all. I am new to physics but am quite competent in maths and other sciences. I am studying Open University's Exploring Science module and this one question has me stumped. I follow all of the instructions but always come to a completely improbable answer. The interesting thing is, that if I divide my answer by 1 million I get the correct answer, which makes me think that I have missed out a line of working somewhere along the line. I looked at the densities of the planets in our Solar System and tried to get the correct answer by the same calculations. Once again, my answer is one million times to large! I was hoping somone with a bit more experience in the field could shed some light for me. The question is:

Callisto, one of the satellites of the planet Jupiter, has a mean radius of
2403 km and a mass of 1.076 × 10 to the power 23 kg. Calculate its mean density in kg m
(i.e. SI units), giving your answer in scientific notation to the appropriate
number of significant figures and showing all of your working


2. Relevant equations

V= 4/3πr3 and p = m/v


3. The attempt at a solution


Cube the radius: (2403km)3 = 1.387590483 x 1010
Multiply that answer by 4: 1.387590483 x 4 = 5.550361931 x 1010
Multiply that answer by π: 5.550361931 x π = 1.743697627 x 1011
Divide that answer by 3: 1.743697627 x 1011 / 3 = 5.812325422 x 1010
Volume of Callisto = 5.812325422 x 1010 km3 = 5.812325422 x 1013 m3

Now that the volume is known - and the mass is provided in the question (1.076 x 1023 kg) - the density can be calculated by the following formula:

Density = mass/volume = (1.076 ×〖10〗^23 kg)/(5.812325422 × 〖10〗^(13 ) m^3 ) = 1.851238398 x 109 kg m-3

If I divide this answer by 1 million, I get the correct answer. But I don't know why!

phyzguy

One km^3 is (10^3 m)^3 = 10^9 m^3, not 10^3 m^3 This is your problem.

Johnboy

Thanks phyzguy, feel a bit stupid now!