# Weighing in With Gravity

How do you feel today? Heavy as a ton of lead, or a ton of feathers? Light on your feet, or dragging on the ground? It probably depends on a lot of things, most particularly your present physical state, and possibly on a pound or two that you’re up, or down, because of holiday eating, or fasting, or a long list of other factors.

Your weight, however, is not just dependent on your diet or your state of mind, but in some measure to physical factors beyond your control, like gravity itself.

Your weight is the product of your actual mass (how much matter is in your body) and the acceleration you experience mostly due to the force of gravity pulling you toward the Earth’s center. At the Earth’s surface the force of gravity is inversely proportional to the square of your distance to Earth’s center of mass. So, if you were twice as far from the Earth’s center as you are now, you’d weight one divided by two squared, or one quarter, as much. Of course that would put you almost 4000 miles into space!

The only thing we ordinary (non-astronaut) humans can do to affect our weight in this way is to climb a mountain, or fly in an airplane, to get farther from the Earth’s center. How much lighter would you be, say by climbing a three mile high mountain, compared to sea level? As it turns out, about 0.2%–so a 150 pound person would weigh about a third of a pound less at the top of Mount Shasta than on Ocean Beach. You’d lose much more weight from the exercise alone….

Places to avoid if you want to lose weight under the gravitational plan would be Earth’s poles, for a couple of reasons. One is that at the poles, even at sea level, you’re about 13 miles closer to the Earth’s center than you are at the Equator. The reason for this is that Earth isn’t a perfect sphere, but an “oblate sphereoid”…in other words, a shape like a ball of playdough that you made into a nice sphere, but then squashed slightly between your palms.

Also, at Earth’s poles you don’t experience centripetal acceleration (the tendency to fly off of a spinning object, be it the rotating Earth or a whirling merry-go-round).

What’s the net weight gain by standing at a pole? About 0.5% heavier, or three quarters of a pound for that 150 pound person.

Finally, there are local variations in the gravity at Earth’s surface caused by differences in the density of the materials in Earth’s crust that account for weight differences of about 0.01%. You probably sweat off more weight than that reading this blog….

Now if you really want to affect a change in weight, go to another planet. Due to differences in the size and mass of other worlds your weight can vary drastically depending on which celestial body you choose to plant your flag on. On Mars you’d weigh 38% of your Earth weight, and on the Moon only about 17%. If you could stand on the surface of a gas giant like Jupiter (say, on the deck of a floating gas mining rig), you’d weight over twice your Earth weight! And on Pluto, you’d weigh less than 7% what you’re feeling right now—maybe as much as your cat.

But back on Earth, the sweet spot for weight loss would appear to be a high mountaintop near the Equator. That would be northern Ecuador; book your flight now! Oh, and if you plan your trip there when the Moon is passing directly overhead, pulling you upward with its own gravity, bonus!

Weighing in With Gravity 5 April,2013

## Author

### Ben Burress

Benjamin Burress has been a staff astronomer at Chabot Space & Science Center since July 1999. He graduated from Sonoma State University in 1985 with a bachelor’s degree in physics (and minor in astronomy), after which he signed on for a two-year stint in the Peace Corps, where he taught physics and mathematics in the African nation of Cameroon. From 1989-96 he served on the crew of NASA’s Kuiper Airborne Observatory at Ames Research Center in Mountain View, CA. From 1996-99, he was Head Observer at the Naval Prototype Optical Interferometer program at Lowell Observatory in Flagstaff, AZ.

Read his previous contributions to QUEST, a project dedicated to exploring the Science of Sustainability.