The Science of Sustainability

Weighing in With Gravity

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Veitimilla Summit, Ecuador

Veitimilla Summit, Ecuador

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!

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Category: Astronomy, Blog

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Ben Burress

About the Author ()

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.
  • Richard Carlson

    UNDERSTANDING DIMENSIONS and GRAVITY:

    I do hope I
    can clearly get my points across without too much confusion.

    Let us start
    with a ball and place it in front of a mirror. We all know that a mirror is
    absolutely bound by only two dimensions; height and width.

    The ball’s
    reflection takes up a particular AREA of the mirror. In other words, it’s
    reflection DISPLACES a given AREA. It will do so as long as there is nothing
    else in the way.

    Thus, the
    second dimension is simply an IMAGE of the third dimension. Think about this
    for a minute before going deeper into my thoughts.

    Now
    remember, if the second dimension had intelligence, it could neither see the
    third dimension nor fathom such a thing; because it has two dimensional eyes
    and two dimensional thinking.

    Well we are
    in the same boat…we do not have 4th dimensional eyes nor 4th
    dimensional thinking.

    The “why?” it
    seems to me, is that we are simply an image of the 4th dimension. To
    put it another way, we are a three dimensional mirror.

    I will not pretend to understand nor visualize
    the concept of how the 4th
    dimension appears or functions; but I
    believe it makes clear to me what GRAVITY really is.

    Depending
    upon the VOLUME, not the mass of an object a certain amount of the 4th
    dimension is being DISPLACED, which we define as GRAVITY.

    EXAMPLE:
    When something is placed into water, it receives water pressure in accordance
    to it’s volume; not it’s mass. Although Jupiter is very large, it’s mass is not
    so great, but it’s gravity is greater than that of Earth….because of the
    greater VOLUME.

    To my
    thinking, it appears there is a parallel between the two examples.

    This is my
    simple explanation of what has baffled scientists for many, many years.

    Remember the Bible tells us that God said, “Let us make man
    in our IMAGE.”

    Please give me your
    opinion: Richard Carlson…1514 Ambrose
    Avenue, Cincinnati, Ohio 45224 E-mail
    address: rac1@fuse.net
    Thanks for your participation.

    • Ben Burress

      Jupiter’s volume (or more specifically, it’s radius) affects the strength of the gravity at its surface by setting how far the surface is from the center of its mass. If you were to squeeze Jupiter to a smaller volume, the surface gravity would increase because the surface would become closer to its center of mass. Similarly, if you increased Jupiter’s radius (and therefore volume), the surface gravity would decrease because the surface would be farther from Jupiter’s center of mass.

      • Richard Carlson

        Then why is earth's gravity not greater than that of jupiter

  • Richard Carlson

    A bag of feathers would fall slower than a bag of rocks, because it would have more volume and thus would encounter more frictional resistance. However, if the feathers could be compressed to the same volume as the rocks, their fall would be the same.

  • Richard Carlson

    Come to think about it, maybe the search for "Dark Matter" is simply apart of the 4th Dimention, since it cannot be seen or even detected. Yet, it is said it must be…somewhere!