[npjlwmqz] Lead or tungsten baseball

density of lead: 11.3 kg/liter

density of tungsten: 19.3 kg/liter

mass of baseball: 5 to 5.25 oz, according to rules.  What is the distribution of masses of baseballs used in actual current MLB play?  Surely manufacturing tolerances are tighter than 5%.  Let's use 5 oz.

diameter of a 5 oz sphere made of lead: 2 * (3/4 * (1/pi) * (5 oz) / (11.3 kg / l))^(1/3) = 1.13 inch

diameter of a 5 oz sphere made of tungsten: 0.95 inch

circumference of baseball (for comparison), according to rules: 9 to 9.25 inch.  Divide by pi to get diameter = 2.86 to 2.94 inch

Inspiration was pitchers throwing balls into the outfield stands.  They practice "long toss".  How much further could they throw with decreased air resistance through smaller cross sectional area?  We probably also want dimples like a golf ball.  (Incidentally golf balls are 1.62 oz and have diameter 1.680 inch.  Ping pong balls have diameter 1.57 inch.)  What weight of a (say) tungsten sphere is optimal for throwing far?  Too light and air resistance slows it down a lot.  Too heavy and you're simply not strong enough to impart a lot of velocity.  Of course, major league velocity and small shape would also make it a dangerous, perhaps deadly, projectile: maybe useful for fiction (variation on Hawkeye).

A lead ball with a surface layer of lead oxide would be bright white like a golf ball, easy to spot after throwing.  But shiny, if that could be done somehow, would also be nice.

Gold has the same density as tungsten.  Maybe award a gold ball as a prestigious baseball prize, worth about $7000.  Gold is not brittle like tungsten, so a ball could probably be thrown hard with less worry about breaking on impact.

Consider using jai-alai-like flexible arm extenders.  What is the ultimate human limit for throwing spheres?  Of course, we'll need to put in some arbitrary restrictions on energy storage.  Previously, on modifying shot put.