How much would you weigh on the ISS?

If you’re reading this blog then chances are you’ve seen at least one video of an astronaut doing something cool on the International Space Station. In all of these videos, it looks like there is no gravity, right? Let’s plug some numbers into Newton’s universal law of gravitation and see if that is actually the case.

Newton famously discovered* that objects with mass attract each other via a force whose strength is inversely proportional to the distance between the objects squared. That means that if the distance between two objects is doubled, the force of gravity between them will be one-fourth as strong. The complete equation for calculating the gravitational force between two objects is:newtons_universal_law_of_gravitation_equation

Where here m1 and m2 are the masses of the two objects in consideration (in this case, you and the Earth), r is the distance between the objects measured from their centers, and G is a special constant of the universe called the gravitational constant. So some useful values for us to consider are:

Quantity Symbol Value
Mass of the Earth me 5.972 x 1024 kg
Radius of the Earth re 6.371 x 106 m
Gravitational constant G 6.674 x 10−11  N · (m/kg)2
Distance to the ISS yISS 400 km
Mass of a typical person mp 80 kg

So if we plug all of these values into the equation to calculate the force of gravity acting on a person on the ISS, it comes out to about 696 N. By comparison the same person standing on the surface of Earth would experience about 786 N of gravitational force. Given my penchant for making graphs, it may come as no surprise that I plotted the force of gravity versus distance away from the surface of Earth using the numbers from the table above. Here’s the result:


All of this means that there is only about 10% “less gravity” on the ISS compared to standing on Earth  far from zero gravity. So what gives!?

The answer to the question “why do astronauts on the ISS appear weightless?” is not all that complicated, but it defies the intuition that many people have. Check out this image from the Newton’s cannonball Wikipedia page:


This image does a great job of explaining what it means to be in orbit. When something is in orbit (such as the astronauts on the ISS), it is really just falling toward the Earth. However it is also moving sideways fast enough that instead of hitting the Earth it misses and continues to fall. Look at the different paths in the picture above: paths A and B represent an object that wasn’t moving quite fast enough to get into orbit, it was falling and hit the Earth; paths C and D represent objects that are in orbit, they are constantly in free fall towards the Earth but they are moving sideways so fast that they never actually hit it; path E represents an object moving sideways so fast that it just flies away from Earth and therefore doesn’t go into orbit. If you want to play around with this, there are lots of interactive Newton’s cannon demos available such as this one.

So in fact the astronauts on the ISS are just constantly in free fall. This means that they don’t experience any contact forces of objects pushing on them (like we do when we’re standing on the ground and it’s pushing up on us). If you’ve ever been on an amusement park ride where you’re dropped to the ground, you experience the same sensation of weightlessness that astronauts on the ISS do, but the difference is it only lasts for a few seconds before the ground gets in the way.


Here is the Python source code to generate the plot in this post. You will need Python 2.7, NumPy, and matplotlib for the script to run.

*Note that the Newtonian theory of gravity is actually an approximation that has since been supplanted by the general theory of relativity. However for the majority of simple calculations such as the one discussed here, the Newtonian theory is a very good approximation and therefore good enough to get the job done.


5 thoughts on “How much would you weigh on the ISS?”

  1. When I initially left a comment I seem to have clicked the -Notify me when new comments
    are added- checkbox and now whenever a comment is added I receive 4 emails
    with the exact same comment. Perhaps there is
    a means you are able to remove me from that service?

    Appreciate it!

  2. I seriously love your blog.. Great colors & theme.
    Did you create this web site yourself? Please reply back as I’m hoping to create my own site and would love
    to learn where you got this from or what the theme is called.

  3. Hello! I understand this is kind of off-topic but I had to ask.
    Does operating a well-established website such as yours take a
    large amount of work? I am brand new to operating a blog but I do write in my journal on a daily
    basis. I’d like to start a blog so I can share my personal experience and
    feelings online. Please let me know if you have any suggestions or tips for brand new aspiring bloggers.

  4. 髪がスカスカになって頭のテッペンが見えるようになってきたとしたら危険信号です。髪の毛が薄くなって禿げる原因にはいろいろありますが、頭皮の環境を整えることで禿げが良くなることもあります。質の良い睡眠を取るなどの生活習慣の見直しとともに、育毛剤を使ってみるのも一つの手です。育毛剤には頭皮を柔らかくして、脱毛の原因を抑制し、頭皮に栄養を浸透させて毛髪の成長を促してくれるものがあるので、そういう育毛剤を使ってマッサージしてみると良いです。使い始めてスグに効果を感じることは少ないかも知れませんが、しばらく使い続けることでよい変化がもたらされることが多いです。

Leave a Reply

Your email address will not be published.