# ISS question **URL:** \ **Category:** Factual Questions\ **Created:** [March 30, 2017, 12:07am UTC](https://boards.straightdope.com/t/iss-question/783319 "2017-03-30T00:07:30Z")\ **Posts on this page:** 6\ **Page:** 1
**Author:** ![zombywoof](https://avatars.discourse-cdn.com/v4/letter/z/9e8a1a/32.png) [@zombywoof](https://boards.straightdope.com/u/zombywoof)\ **Post date:** [March 30, 2017, 12:07am UTC](https://boards.straightdope.com/t/iss-question/783319/1 "2017-03-30T00:07:30Z")
Last night I watched an ISS flyover from my backyard - it passed almost directly overhead, reaching a maximum height of something like 88 degrees - which made me wonder: Say the ISS makes a theoretical pass from my viewpoint from the horizon to directly 90 degrees overhead to the opposite horizon. At the points at which it crosses the horizon for me (“rising” and “setting”), it would be directly overhead potential observers at other locations - the question is, how far away from me would they be? ---
**Author:** ![Trinopus](https://avatars.discourse-cdn.com/v4/letter/t/2bfe46/32.png) [@Trinopus](https://boards.straightdope.com/u/Trinopus)\ **Post date:** [March 30, 2017, 12:49am UTC](https://boards.straightdope.com/t/iss-question/783319/2 "2017-03-30T00:49:07Z")
Oh! At first, I thought this was just “how far away is the horizon.” But not quite! Basically, you draw two circles: one is the earth, and the other is the ISS orbit. You draw a tangent line across the inner circle to the outer circle, and then drop verticals from those intersection points to the earth’s surface. All very easy to do graphically. Using geometry and equations and stuff is harder… Anyway, nifty question! ---
**Author:** ![Kimble](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kimble/32/19185_2.png) [@Kimble](https://boards.straightdope.com/u/Kimble)\ **Post date:** [March 30, 2017, 1:09am UTC](https://boards.straightdope.com/t/iss-question/783319/3 "2017-03-30T01:09:30Z")
Let O be the center of the Earth, which I’ll assume is spherical. Let U be your location on Earth. Let I be the location of the ISS when it hits the horizon. Then, triangle IOU is a right triangle where: side OU = the radius of the Earth (3959 miles) side IO = OU + the height of the ISS’s orbit (3959 miles + 249 miles = 4208 miles) angle IOU in radians = the distance we want in Earth radii. Breaking out the simple trigonometry, angle IOU = arccos(OU/IO) ≈ 0.3457… radians. Multiplying that by the radius of the Earth ≈ **1369 miles** , a _lot_ further than I would have guessed. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [March 30, 2017, 1:21am UTC](https://boards.straightdope.com/t/iss-question/783319/4 "2017-03-30T01:21:19Z")
Actually, this _is_ just “how far away is the horizon”… But it’s how far away the horizon is at the height of the ISS, not your height. Well, actually, strictly speaking, it’s the sum of your horizon distance and the ISS’s, but its horizon is so much larger that yours is insignificant. ---
**Author:** ![snfaulkner](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/snfaulkner/32/433_2.png) [@snfaulkner](https://boards.straightdope.com/u/snfaulkner)\ **Post date:** [March 30, 2017, 1:27am UTC](https://boards.straightdope.com/t/iss-question/783319/5 "2017-03-30T01:27:14Z")
> [@Chronos](#): > > … yours is insignificant. Why does everyone keep saying this to me? ---
**Author:** ![standingwave](https://avatars.discourse-cdn.com/v4/letter/s/9de0a6/32.png) [@standingwave](https://boards.straightdope.com/u/standingwave)\ **Post date:** [March 30, 2017, 9:28am UTC](https://boards.straightdope.com/t/iss-question/783319/6 "2017-03-30T09:28:54Z")
> [@Chronos](#): > > Actually, this _is_ just “how far away is the horizon”… But it’s how far away the horizon is at the height of the ISS, not your height. > > Well, actually, strictly speaking, it’s the sum of your horizon distance and the ISS’s, but its horizon is so much larger that yours is insignificant. This is true, the adding together of horizons. The map of the satellite’s horizon is also known as its footprint so you can get a pretty good idea by googling for [ISS footprint](https://www.google.com/search?q=ISS+footprint).