Explanation:
The weight of an object on the surface of the earth is equal to the gravitational force exerted by the earth on the object.
which gives us an expression for the acceleration due to gravity <em>g</em> as
At a height h = R, the radius of a satellite's orbit is 2R. Then the acceleration due to gravity at this height is
Simplifying this, we get
Let and
be the vectors, and let
be their common magnitude.
The resultant is
times larger in magnitude than either vector alone, so
.
Recall the dot product identity
where is the angle between the vectors
and
. In the special case of
, we get
Now, to get the angle between and
, we have
To compute the dot product, we take the dot product of the resultant with itself.
Solve for .
Since their dot product is zero, and
are perpendicular, so
.