Question

Uranus (better known as Caelus to those in the know who prefer properly consistent naming conventions for planets) is a massive ice giant planet with a diameter of 51,118 kilometers and a mass of 8.685 × 1025 kilograms (over 4 times Earth’s diameter and 14.5 times Earth’s mass). The small, rocky-metallic terrestrial planet Venus is smaller than planet Earth, with a mass of 4.869 × 1024 kilograms and a diameter of 12,104 km. Which planet has the strongest surface gravity (and where would you feel like you had the greatest weight?)

Answer 1

8.87 m/s^2

Is the same for both planets

Step-by-step explanation:

Hello!

The surface gravity can be calculated from Newton's Law of Gravitation and Newton's Second Law :

ma = F =G Mm/r^2

Solving for a:

a = G M/r^2

And the surface graity g = a(R), that is, the surface gravity is equal to the acceleration evaluated at the radius of the planet:

g = G M/R^2

Since G is a constant, we need to evaluate M/R^2 for both to know in which planet the surface gravity is the geratest:

M_u/R_u^2 = 1.323 x 10^11 kg/m^2

M_v/R_v^2 = 1.323 x 10^11 kg/m^2

It turns out that the surface gravity in both planets is the same! which is:

g = G M_u/R_u^2

= ( 6.67408 × 10-11 m^3 / (kg s^2) ) *( 1.323 x 10^11 kg/m^2)

= 8.87 m/s^2

*as you can check on google*

You would feel the same weigth in both planets, however you wil feel lighter in these planets than in earth.