What would be the gravitational force that a planet with the same density as Earth and having twice Earth's radius exerts on a 59.1-kg astronaut?
A)580 N
B)290 N
C)1160 N
D)2320 N
E)1200 N

Question

Quizplus · Accepted Answer

We can use the formula for gravitational force:

F = G * (m1*m2)/r^2

Where:
 G = gravitational constant (6.67 x 10^-11 N*m^2/kg^2)
 m1 = mass of planet
 m2 = mass of astronaut
 r = distance between planet's center and astronaut's center

First, let's find the mass of the planet:

density = mass/volume
4/3 * π * r^3 * density = mass
4/3 * π * (2*6371 km)^3 * 5.5 g/cm^3 = 1.08 x 10^25 kg

Now we can plug in the values:

F = G * (m1*m2)/r^2
F = 6.67 x 10^-11 * (1.08 x 10^25 * 59.1) / (2*6371 km)^2
F = 1160 N

Therefore, the gravitational force that the planet exerts on the astronaut is 1160 N.

What Would Be the Gravitational Force That a Planet with the Same