Solution

2.    Use Newton's law of gravity to compute your weight on Earth, Mars, the asteroid Ceres, Jupiter (ignore gas...)

 

        (a) For Earth, assume your mass is 100 kg.  Using Newton’s law of gravity;

      

F = 6.67 x 10^-11 x 5.97 x 10²⁴ x 100/(6.378x10⁶)²      

 

F = 978 N.  With 4.45 N in a pound, this gives F = 220 lbs

 

       (b) For Mars

 

Similar calculation to get F = 86 lbs

 

       etc.

 

5.  Suppose the average mass of each of the 7000 asteroids in the solar system is about 10¹⁷ kg.  Compare the total mass of all asteroids with the mass of Earth.

The total mass of all asteroids would be 7000 x 10¹⁷ kg = 7*10²⁰ kg.  The mass of Earth is about 6x10²⁴ kg.  Comparing these, 6x10²⁴ kg / 7x10²⁰ kg = 8,600.  Thus, Earth has 8,600 times more mass than all the asteroids combined.  As we see them today, the asteroids would not make up much of a planet.

 

6.  Assuming a roughly spherical shape and a density of 3000 kg/meter cubed, estimate the diameter of an asteroid having the average mass given in the previous question.

 

3000 kg/m³ = 10¹⁷ kg / 4/3p(R)³.  R = 20,000 m = 20 km.  Diameter = 40 km.