How far can you see?

It’s been over a decade since I read Kim Stanley Robinson’s quite epic novel Red Mars, but I remember one particular paragraph quite well. One character had just set foot on Mars for the first time and noted how the horizon seemed closed, and so it was obvious they were standing on a smaller planet. Which made me wonder… would you actually be able to notice that?

I’ve always loved looking out towards the horizon. Especially by the shore on those beautifully clear days when you can see right to the edge of the sky. But just how far away is the horizon anyway? Actually, it’s pretty easy to calculate.

Over the hills and far away...

A fairly simply bit of trigonometry, and it works out that this equation is all you need. Here, d is the distance to the horizon, h is your height off the ground, and R is the radius of whatever planet you happen to be standing on. Of course, this assumes that there are no hills or other objects between you and the horizon, so it only works properly over vast flat expanses. So assuming your eyes are about 5’7 above the ground (average for a human being), and taking Earth’s radius to be 6378.1 km, that means the horizon you see is 4.66 km away. Perhaps a little closer than you might expect.

Mars, on the other hand, is indeed a much smaller planet. The radius of Mars is only 3397 km, which means that from the same height, the martian horizon would appear 3.40 km away.

The Moon is even smaller with a radius of only 1737.4 km, meaning on the moon, the horizon is only 2.43 km away. Take a closer look at those Apollo photographs from the surface of the Moon. You can actually see that. If you were standing on the Moon, you really would notice that it’s much smaller than Earth!

About Invader Xan

Molecular astrophysicist, usually found writing frenziedly, staring at the sky, or drinking mojitos.
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10 Responses to How far can you see?

  1. esdmattroush says:

    And here all the nutters who think we faked all the moon landings said the horizon looked close because it was all done on movie sets…

  2. Lester says:

    What’s up, after reading this awesome post i am as well delighted to share my know-how here with friends.

  3. Indy says:

    Great article. It seems to me that a closer horizon would make it easier to get lost since landmarks would pass beyond your vision sooner than on Earth. Future Martian astronauts should keep this in mind.

  4. Manuel says:

    Hello Invaderxan!

    A really nice and interesting article. I will try to solve this, but I think I have some problems to understand what “h” is. Would you help me? Thanks ^^

    • invaderxan says:

      h is your height above the ground. Simple as that.

      For the distances I’ve calculated here, I’ve taken it to be about 170 cm (or 5’7) because on average, that’s how far most peoples eyes are from the ground when they stand up.

      It makes a difference, because if you’re higher up you can obviously see a lot further, so the horizon will appear more distant if you’re, standing on a cliff, in a tall building, looking from an aeroplane window, etc.

      Does that help? :)

  5. Baribal says:

    You, sir, have a good taste in literature. Can you also check Sax Russells hypothesis that Mars’ atmosphere should be milky white after terraforming? :)

    • invaderxan says:

      Why thank you, my friend! :)
      Sax Russell… White atmosphere… I don’t recall that one. I’ll have to have a look for it. Thanks for the tip!

      Edit–– And after a few cursory Google searches, I can’t find it referenced anywhere. I guess I may have an excuse to re-read the books sometime…

      • Baribal says:

        It’s near the very end of Red Mars (IIRC), when Russell and several others ride a car along a raging river. Russell, being who he is, watches it through the cameras and calculates a lot of stuff.

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