Answer:
To find the weight of the box on the planet, we need to use the equation for gravity:
F = G * (m1 * m2) / r^2
where F is the force of gravity, G is the gravitational constant (approximately 6.67 x 10^-11 N * (m/kg)^2), m1 is the mass of the first object (in this case, the box), m2 is the mass of the second object (in this case, the planet), and r is the distance between the two objects.
First, let's find the mass of the planet:
m2 = 2 * 5.97 x 10^24 kg (mass of the Earth) = 11.94 x 10^24 kg
Next, let's find the radius of the planet:
r = 1/3 * 6.37 x 10^6 m (radius of the Earth) = 2.123 x 10^6 m
Finally, let's use the equation for gravity to find the weight of the box on the planet:
F = (6.67 x 10^-11 N * (m/kg)^2) * (20 N * 11.94 x 10^24 kg) / (2.123 x 10^6 m)^2
F = 20 N * (2 * 11.94 x 10^24 kg / (2.123 x 10^6 m)^2 / 6.67 x 10^-11 N * (m/kg)^2)
F = 20 N * (2 * 11.94 x 10^24 kg / 4.8869 x 10^13 m^2)
F = 20 N * 2.43 x 10^11 N
F = 48.6 N
So the weight of the box on the planet would be 48.6 N.
Step-by-step explanation: