Question

a

Answer 1

If I call with m the mass of an object upon the earth surface, then its weight W is:
\[\Large W = \frac{{GMm}}{{{R^2}}}\]
where G is the Newton's constant, M is the earth mass, and R is the earth radius

Answer 2

now, if I call with h, the requested height then I can write:
\[\Large \frac{W}{{16}} = \frac{{GMm}}{{{{\left( {R + h} \right)}^2}}}\]

Answer 3

substituting W, we have:
\[\Large \frac{1}{{16}}\frac{{GMm}}{{{R^2}}} = \frac{{GMm}}{{{{\left( {R + h} \right)}^2}}}\]

Answer 4

and after a simplification, we can write:
\[\Large \frac{1}{{16}} = \frac{{{R^2}}}{{{{\left( {R + h} \right)}^2}}}\]
or:
\[\Large \frac{1}{{16}} = {\left( {\frac{R}{{R + h}}} \right)^2}\]
and finally:
\[\Large \frac{1}{4} = \frac{R}{{R + h}}\]
please solve the last equation for h

Answer 5

that's right!
it is
h=3*R=3*6400= 19200 Km

Answer 6

ok!

Answer 7

thanks! :)