Imagine a string tied tightly around Earth’s circular equator (of radius about 6400 km) and then add 1 m of extra length to it. Pinch it at a point and lift it up from the surface. How high can you lift it?

Imagine that the "pulled" (pinched up) part of the string subtends an arc of 2*theta (in radians) between the points of tangency of the string to the earth.  Converting all units to meters gives:  2*6400000*theta + 1 = 2*6400000*tan(theta).  Using excel to solve gives theta = 0.0061656402 radians.  The height of the pinch is then 6400000/cos(theta) - 6400000 , or about 121.7m<table width="103" style="border-collapse: collapse;width:77pt" border="0" cellspacing="0" cellpadding="0"> <colgroup><col width="103" style="mso-width-source:userset;mso-width-alt:3766;width:77pt"> </colgroup><tbody><tr height="20" style="height:15.0pt"> <td width="103" height="20" align="right" style="margin: 0px; border: 0px rgb(0, 0, 0); width: 77pt; height: 15pt; background-color: transparent;">
</td></tr></tbody></table>

Posted by Kenny M on 2018-10-29 21:22:39