Green Spacesuit

I’m happy to report that golf fans here on simulated Mars are increasing in number!  With the recent adventure of hitting golf balls in our spacesuits (see last post) and our watching the Masters Tournament this weekend, the entire crew has developed a burgeoning interest and baseline understanding of golf.

The Masters, the first major PGA tournament of the year, is played at Augusta National golf club, a prestigious, private golf course with only 300 members; the club is invitation only, with members including Bill Gates and Condoleezza Rice. Each of these members receives a green sport coat with the club logo. This iconic green jacket is also awarded to the champion of the Masters tournament each year. Perhaps, golf champions on Mars should be awarded with a green spacesuit!

Jordan Spieth, 2015 Masters Champion (Photo: Jamie Squire/ Getty Images)

One of the signature sections of Augusta National is known as “Amen corner” which is a stretch of three holes that have been the stage for much drama over the years. This corner of the course begins with Number 11 “White Dogwood,” the longest and most difficult Par 4 on the course. It's 505 yards from the starting tee to the middle of the green, whereas the other Par 4 holes are on average about 440 yards. The 2015 Masters champion, Jordan Spieth, has an average drive distance of about 295 yards, so after an average drive, he’d have a 210-yard approach shot into the 11th green.. how would this differ on Mars?

Since Augusta National is seated on land that was formerly a plant nursery, each hole has a name that reflects the plant life decorating the hole. I can only imagine a red, desert-like landscape for a Martian golf course, so the calculations below should be further refined to account for differences in the distance that a ball rolls on carefully manicured grass versus hitting the dust-covered, rocky surface of Mars.  However, if 295-yard drives on Earth would carry 635 yards on Mars, here's the Martian equivalent of Augusta National:

The physics of golf is actually simpler on Mars. Without an atmosphere, Mars has just 1% of Earth's air density. Thus, aerodynamic forces such as lift and drag are trivial on Mars with magnitudes less than 10e-6. Simple projectile motion equations that only consider gravity are appropriate for computing the trajectory of a golf ball on Mars.  Opposed by only about 1/3 of Earth's gravity, every Mars explorer could hit the ball further than PGA tour players on Earth!

The club head speed of a tour player swinging a driver ranges from 100-150 mph. On Earth and Mars alike, momentum and kinetic energy are transferred from the golf club to the less massive golf ball, resulting in an initial velocity for the golf ball that is higher than the velocity of the golf club.  Most of the energy sets the ball into motion, but some of this kinetic energy is lost as the club hits the golf ball; this is accounted for by the coefficient of restitution (which USGA rules dictate should be less than 0.83).  An expression for the initial velocity of the golf ball is found by combining and simplifying the conservation of energy and momentum equations:

If we assume that velocity of the club head is 55.8 m/sec (125 mph), mass of the golf ball is .0459 kg, and mass of the club head is 0.195 kg, then the initial velocity of the golf ball is 82.7 m/sec (185 mph).

The projectile motion of the golf ball can be calculated based on the initial velocity of the ball and the launch angle.  A standard driver has a loft angle of about 9 degrees; however, the driver connects to the ball on the upswing of the pendulum motion of a golf swing adding about 3 degrees of loft. After combining the kinematics equations for both the x and y directions, the distance traveled by a golf ball on Mars is given by:

With an initial golf ball velocity of 82.7 m/sec and launch angle of 12 degrees, the distance traveled by a golf ball on Mars would be 748 meters or 818 yards!  

Let’s compare to the golf ball that I recently hit on simulated Mars (see last post).  I was restrained by my spacesuit and only hit my 7-iron about 90 yards, instead of the usual 135 yards when freely swinging.  Using simple projectile motion to analyze the corresponding differences in club head speed, I lost about 6.8 m/s (15.2 mph) from swinging in a spacesuit. Even with the handicap of a spacesuit, a tour player on Mars would hit 635-yard drives!  Better yell FORE!

Watch my swing in a spacesuit at https://youtu.be/B2Bm1miYTi8