Question

Imagine a new planet which is 4 times Earth’s mass and measures half of the it’s radius. Now you
have an object that weighs 180 N on Earth’s surface, when we take it to a height of 1600 km
above the surface of the new planet. Find the weight of the object at that location. (Assume the
value of g = 10 m/s2 )

Answer 1

$\boxed{\large{\red{\tt{g'=g[\frac{R²}{(R+h)²}]}}}}$

$\boxed{\large{\red{\tt{g'=\frac{g(\frac{6400}{2})²}{(\frac{6400}{2}+1600)²}}}}}$

$\boxed{\large{\red{\tt{g'=\frac{g×6400×6400}{4800×4800}}}}}$

$\boxed{\large{\red{\tt{g'=\frac{16g}{9}}}}}$

$\boxed{\large{\green{\tt{W(at\:1600km)=mg'}}}}$

$\boxed{\large{\green{\tt{W(at\:1600km)=m×\frac{16}{9}×g}}}}$

$\boxed{\large{\green{\tt{W(at\:1600km)=\frac{16}{9}×180N}}}}$

$\boxed{\large{\green{\tt{W(at\:1600km)=320N}}}}$