Bart weighs 400N on a planet with a radius of 4000km where g= 8.0 m/s/s. What is the mass of the planet?

Question

Anybody know how to do this? I need help/ an answer ASAP! THANKS (:

Answer 1

Newton's Law of Gravity

Acceleration of gravity near the surface of a planet = ( G ) ( Mplanet ) / ( Rplanet )²

Plug in the values given ( convert the radius to meters first ) and solve for Mplanet. Bart's weight is irrelevant unless you want to know his mass.

Answer 2

Bart's weight is equal to the force of gravity between Bart and this planet. Let M be the mass of the planet and m be the mass of Bart. We can then use Newtons force of gravity equation:
F=GMm/r^2
M=F(r^2)/(Gm)
But we need Bart's mass. We can get it from F=ma:
m=F/a
m=400/8.0
m=50 kg
Now back to where we were:
M=F(r^2)/(Gm)
M=(400 N)*((4000 km)^2)/(G*50 kg)
M=1.91817773 × 10^(24) kilograms
or M=1.9*10^(24) kg
note that G is a constant equal to 6.67300 × 10-11 in SI units.