Cool Math for Kids But Not Cool Science

We all know that there is a lot of wrong information out there on the Internet. However, what you may not be aware of is that there are websites that appear to be reputable, which also disseminate bad information. The purpose of this article is to demonstrate that seemingly reputable educational websites exist that teach science that is wrong at a very fundamental level.

The suite of websites led by (and associated websites,, is extremely popular, with 1.2 million unique visitors per day, and 20 million unique visitors per month. These are staggering numbers. The websites teach mainly math and are used by students, parents, and teachers. The websites include an extensive collection of math games for kids, some of which are not free. There are also some webpages on science, and there is one page in particular about gravity that is extremely disappointing. The webpage explains why astronauts that are shown in spacecraft that are in orbit around the Earth are weightless and float around the spacecraft. To quote, the webpage says, “When you see movies with astronauts in space and they are floating all around, it's because they aren't close enough to the Earth (or to another planet) to get pulled down by gravity.” This explanation is completely wrong and it can be shown to be wrong by a 9th-grade student who has studied physics correctly. An elementary application of Newton's law of gravitation, which was discovered more than 300 years ago, shows that the reduction in weight is way too small to explain the effect (I will demonstrate this below).

Educational websites have a certain responsibility to students and parents. Breaching this responsibility is even more serious for websites such as the cool math for kids suite because the number of users is huge. If a child learns about gravity from cool math for kids she will be guaranteed to fail to understand gravity. If she wants to study physics, engineering, or a related discipline later, she will have to unlearn what she learned from cool math for kids. There is absolutely no excuse for teaching science that is wrong at such a basic level. What is particularly disturbing is that there must be thousands, if not more, science teachers who have visited the cool math for kids gravity page and not a single one has persuaded the owners to correct the page or remove it. (I was told, “We will look into it.” This is very puzzling because any elementary physics book can show that the information on the webpage is wrong.)

Why Are Astronauts in Space Weightless (or Why Do They Float Around?)

So, what is the real reason why astronauts are weightless in spacecraft in orbit around the Earth, and are able to effortlessly float around? First, I will demonstrate why the cool math for kids explanation is wrong. In the diagram below the white curve shows the weight of an object (which could be a person) at a height above the Earth's surface in kilometers (km). The weight is shown as a percentage of the weight that the same object would have on the surface of the Earth. If an object is truly weightless in a spacecraft, this percentage should be zero (or at least very small, less than 10 percent or so). As a concrete example, let's suppose that we are talking about an astronaut on the international space station (ISS). According to Wikipedia, the height of the ISS above the Earth's surface varies between 278 km and 460 km. On the diagram I have shown vertical lines corresponding to these extrema in height and I have then drawn horizontal lines to show, according to Newton's law of gravitation, what percentages of the astronaut's regular weight that the two height extremes correspond to. We see that the astronaut's weight is never less than 87.5% of her weight on the Earth's surface. This 13.5% reduction in weight is far from a state of being weightless and could certainly not allow astronauts to float around as they do.

Effective weight above the surface of the Earth which coolmath4kids should easily be able to calculate

The real origin of an astronaut's weightlessness is that objects that are in a state of orbit under gravity are in a state of free fall. All objects free fall with the same acceleration regardless of mass (it is a fundamental law from physics, grounded in observational fact). Therefore astronauts in an orbiting spacecraft are continually falling towards the Earth but the spacecraft is also falling with the same acceleration so there is no reason for an astronaut to be bound to the floor of a room in the spacecraft (or any other part of it). Neither the astronaut nor the spacecraft fall to the Earth's surface because both the astronaut and spacecraft have a tangential velocity as well. So they fall a little bit but move tangentially at the same time, gaining a bit of height over a new bit of Earth: the laws of physics determine the radius of the orbit in such a way that the fall in height is exactly compensated by the tangential motion. For the same reason, the moon is in free fall towards the Earth but it never hits the ground. If something caused it to lose energy, then it would fall closer to Earth.

So, what is weight exactly? An object only has weight if its free fall is somehow impeded. Free fall under gravity, and zero weight, is the natural state of an object. However, if the free fall is impeded, the object has weight. For example, you standing on the ground have weight because your free fall towards the center of the Earth is impeded by the ground. Your weight is equal to the force exerted by the ground that exactly balances your need to free fall. If the ground gave way, you would suddenly become weightless. In an elevator your weight changes because the acceleration of the elevator affects your tendency to free fall.

You should now see that the wrong explanation of weightlessness given by cool math for kids can be shown to be wrong even without the detailed application of Newton's equation for gravitational force. You see, in order for the astronauts and the spacecraft to orbit at all, a gravitational force is required. If the gravitational strength were negligible, as the cool math for kids gravity page would have you believe, the spacecraft could not orbit Earth in the first place!

Finally, I point out that even the Wikipedia page that talks about weightlessness on the space station demonstrates a lack of understanding of gravity. The Wikipedia page states “Gravity is the only significant force acting upon the ISS, which is in constant free fall. This state of free fall, or perceived weightlessness, is not perfect however...” The point is that the reduced weight is not just perceived, it is the weight. The weight of an object has nothing to do with its mass. It is entirely dependent on an object's state of motion and the various forces acting upon it.

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