{"id":1193,"date":"2009-05-01T17:39:52","date_gmt":"2009-05-01T22:39:52","guid":{"rendered":"http:\/\/www.spaceelevatorblog.com\/?p=1193"},"modified":"2009-05-01T17:44:27","modified_gmt":"2009-05-01T22:44:27","slug":"using-a-space-elevator-to-generate-1g","status":"publish","type":"post","link":"https:\/\/www.spaceelevatorblog.com\/?p=1193","title":{"rendered":"Using a Space Elevator to generate 1g…"},"content":{"rendered":"

Someone commented with an interesting question on a YouTube video<\/a> I posted last year:<\/p>\n

“I wonder how far from the earth the end of the cable would have to be to allow for the equivalent of 1G due to centrifugal force.”<\/em><\/p><\/blockquote>\n

I didn’t know so I asked Ben Shelef, CEO of the Spaceward Foundation<\/a> (host of the Space Elevator Games) – this was his reply:<\/p>\n

At any point on the tether, in your reference frame, you have two forces (accelerations) acting on you.\u00a0 Gravity downwards, and the centrifugal acceleration outwards.<\/em><\/p>\n

Gravity diminishes with distance square, so at a height of 6000 km, you’re at double the distance from the center of the earth as you were when you took off, and so the force of gravity is 1\/4 what it was.<\/em><\/p>\n

At ground level, the centrifugal acceleration is very small, but it increases linearly with the radius.\u00a0 (a=omega^2*r)\u00a0 [omega is the spin rate of the Earth].<\/em><\/p>\n

At GEO, the two accelerations are equal. (and each is very small, basically 1\/50g)<\/em><\/p>\n

So as we move out, at some point, the outwards acceleration will equal 1g.\u00a0 how far?\u00a0\u00a0 We can neglect gravity, since it diminishes even further.\u00a0 The Centrifugal acceleration has to increase a factor of 50!\u00a0 So 50 times as far as GEO – way beyond the end of a 100,000 km long tether.<\/em><\/p>\n

Using numbers;<\/em><\/p><\/blockquote>\n