If you stand here on the surface of the Earth, whether at the north pole where the acceleration is greatest or at the summit of Huascarán where it’s the smallest, you’ll be pulled toward the center of the Earth with an acceleration of 9.8 m/s²: the acceleration due to gravity, or “1 _g_” on the surface of the Earth. Sure, there are tiny variations that will ensue, as your distance from Earth’s center, the speed of the planet’s rotation beneath your feet, and the density and composition of Earth’s crust and mantle aren’t constant, but those variations only lead to variations in the gravitational acceleration at the less-than-1%-level. That’s why, if you bring a scale to any of those locations on Earth’s surface and stand on it, you’ll find that the reading on that scale gives you your weight from a very simple formula: your mass (m) multiplied by the acceleration of gravity (1 _g_) on Earth’s surface.
If you have a mass of 100 kg, that means your weight will be 220.5 pounds, or 980 newtons, depending on which measuring system you use. But for an astronaut in space, whether on the International Space Station or on their way to or from the Moon, they’re completely weightless: their weight is zero. That’s what Graeme Cree wants to know, writing in to ask: “Gravity reduces in force the farther you get from the source, of course.
If the attraction is ‘X’ at one location, and you double the distance from the source, the attraction will only be ‘¼X’. Okay, so my understanding is that you measure the earth’s attraction from the core of the earth. At Sea Level I’d be about 4,000 miles from the core.
So, if my weight is 160 at Sea Level, and I moved another 4,000 miles farther away from the Core, my weight should be 40. But in that case, why are we weightless in orbit, only a hundred miles or so from sea level?” This simple-sounding question is actually quite profound, and gets at the heart of what the relationship between acceleration and weight actually is. Let’s figure it out together.
This scale, from more than 100 years ago, balanced out the downward force of gravity exerted by the objects atop the scale with an internal spring. The amount that the spring compresses is dependent on the downward force from the weights above it. If either the mass or the acceleration of the above weights change, so will the reading of the scale.
Wherever you are on Earth, it’s true: gravity always accelerates you downward, toward the center of the Earth, at a rate of 1 _g_: 9.8 m/s². However, you don’t always actually accelerate at that rate! In fact, you’re probably not accelerating downward at that rate right now.
Extract — continue reading at the source.
