Skip to main content

Gravity Around the Globe


We all know that the constant "g" refers to 9.8 m/s^2, the acceleration of objects due to the field of gravity on Earth. But what if I were to tell you that "g" may not be as constant as you thought it was?

Some important values: 

MEarth = 5.972 x 10^24 kg
REarth = 6.371 x 10^6 m
hEverest = 8,848 m
hMariana = -10,994 m

And the equation that will be used: 

g= GME / R^2

where R is the radius of the earth plus the height of each location: (RE+ h)

Now let's find the value of "g" atop the summit of Mount Everest, which is 8,848 meters above sea level.

Image result for mount everest
Fun fact (if you didn't already know it): Mount Everest is not the tallest mountain on earth! You heard me correctly, the tallest mountain is actually Mauna Kea in Hawaii. From base to summit, Mauna Kea is about 10,200 meters high, a whole 3,352 meters taller than Everest! However, since Mauna Kea is partially underwater, and its peak only rises to 4,205 meters above sea level, Mount Everest often takes credit as the highest mountain on Earth.

g= GME / (RE + hEverest)^2
g= (6.67 x 10^-11)(5.972 x 10^24) / (6.371 x 10^6 + 8,848)^2
g= 9.78645 m/s^2

So the value of "g" at the top of Mount Everest is actually about 0.014 m/s^2 smaller than the 9.8 m/s^2 that we all know and love. This makes sense though, because the peak of Everest increases the radius, so "g" becomes weaker. 

Next, let's find "g" at Challenger Deep in the Mariana Trench, the deepest known part of the Earth's crust. It's 10,994 meters below sea level. 

Image result for mariana trench challenger deep

g= GME / (RE + hMariana)^2
g= (6.67 x 10^-11)(5.972 x 10^24) / (6.371 x 10^6 - 10,994)^2
g= 9.8476 m/s^2 

At Challenger Deep, the difference in "g" is a whopping 0.04 m/s^2. Once again, this seems logical because is it closer to the earth's core, so the radius decreases, and "g" should go up. 

The force of gravity can also be affected by locations on the surface of the earth, not just the distance from the center of the earth. This is due to the centrifugal force created by the earth's rotation. The earth rotates around its axis through the North and South Poles, so the poles hardly spin while the equator spins much quicker. Since centrifugal force = mv^2 / r, if v increases (like at the equator), the force will increase, and if v decreases (like at the poles), so will the force. Centrifugal force goes outward from the earth's surface, opposing the force of gravity that draws inward to the earth's core. Therefore, the centrifugal force cancels out some of the force of gravity. At the equator, there is more centrifugal force, so there is less gravitational force. At the poles where there is less centrifugal force, there is more gravitational force. 

Another factor of gravity is the earth's shape. Believe it or not, Earth is not spherical, but flat. 

Image result for flat earth

I'm joking. Sorry to all the flat-earthers out there... and everyone reading this really. 

No, the earth is not perfectly spherical (or flat), but it is in the shape of an oblate spheroid. 


The equator actually bulges out a little due to centrifugal force. The radius of the earth at the equator is about 6,378 km, while at the poles the radius is about 6,257 km. As we saw earlier, when the radius increases, the force of gravity decreases, and vice versa. At the equator, the force of gravity lessens, while at the poles, the force of gravity increases.

Taking into account both the rotation and shape of the earth, at the equator, "g" is 9.78 m/s^2 and at the poles it's 9.83 m/s^2.  

So there you go! While a value of 9.8 m/s^2 may be approximately constant around the globe, it's not always true. 

http://curious.astro.cornell.edu/about-us/42-our-solar-system/the-earth/gravity/94-does-your-weight-change-between-the-poles-and-the-equator-intermediate'

http://wtamu.edu/~cbaird/sq/2014/01/07/do-i-weigh-less-on-the-equator-than-at-the-north-pole/


Comments

Post a Comment

Popular posts from this blog

Physics of Sound Dampeners and Active Noise Cancellation

Physics of Sound Dampeners and Active Noise Cancellation Sound dampening foam panels in a recording studio. ANC headphones worn by pilots and/or passengers in consumer aviation aircraft.  Acoustic treatment of soundscapes has grown alongside the sound production industry. Whether through absorption panels, diffusors and cloud panels to treat a space or headphones placed directly over the ears of listeners, acoustic treatment comes in many forms. Environments are treated acoustically to absorb excess sound to prevent sound levels from crossing a threshold above which the desired goal cannot be had. Before getting into sound dampening, we must discuss sound. Sound is produced when an object vibrates (a form of oscillation) and temporarily displaces nearby air molecules causing a wave effect as the displaced molecules collide with their neighboring molecules. Sound waves are fluctuations in pressure as the initial displacement of molecules experiences collisions that in ...
Post a Comment
Read more

Large Hadron Collider

The Large Hadron Collider (LHC) is the world’s largest and most powerful particle accelerator. The LHC is the largest machine in the world. It took thousands of scientists, engineers and technicians decades to plan and build, and it continues to operate at the very boundaries of scientific knowledge. It first started up on 10 September 2008, and remains the latest addition to CERN’s accelerator complex. The LHC consists of a 27-kilometre ring of superconducting magnets with a number of accelerating structures to boost the energy of the particles along the way. Map of LHC (located in Geneva, Switzerland) Thousands of magnets of different varieties and sizes are used to direct the beams around the accelerator.  Just prior to collision, another type of magnet is used to "squeeze" the particles closer together to increase the chances of collisions. The particles are so tiny that the task of making them collide is akin to firing two needles 10 kilometres apart with suc...
Post a Comment
Read more

Aerodynamics of a Golf Ball

One may wonder how a small golf ball can travel at incredibly high speeds for such long distances.  While the swing of the club is a major component, the structure of the golf ball is quite important.  Unlike a baseball or tennis ball, a golf ball has dimples all over it (usually 336 dimples).  These dimples allow the golf ball to travel without facing much air resistance.  This diagram shows how air travels around the golf ball. The dimples on the golf ball also prevent drag that would occur in the wake region, resulting in further distance.  Also due to the contact with the club during the swing, the golf ball has backspin during its entire flight.  This diagram shows the motion of the golf ball mid flight with the lift force of F. There are hundreds of different types of golf balls that a player can choose.  Some show little affect to a player's game while others can alter their performance completely.  Personally, I prefer Callaway Supers...
Post a Comment
Read more