A newly discovered planet 581c, has a mass 5 times that of the Earth's mass and a diameter one and a half that of the Earth.
If the Earth's gravitational field strength is 9.81N/Kg, what is planet 581c's gravitational field strengh?
For a mass m on Earth, the acceleration due to the gravitational force of attraction is m*g = G*Me*m/r^2, where G is the gravitational constant, Me is the mass of the Earth, and r is the radius of the Earth.
For planet 581c, the mass is 5 times that of the Earth and the diameter is 1.5 times that of the Earth.
A mass m, on the surface of the planet would experience an acceleration due to the gravity of the planet given by:
m*gx = G*5*Me*m/(1.5*r)^2
=> gx = G*5*Me/(1.5*r)^2
we have g = G*Me/r^2
=> gx = [5/(1.5)^2]*G*Me/r^2
=> gx = 5/(1.5)^2*9.81
=> gx = 21.8 m/s^2
The planet's gravitational field strength is 21.8 N/kg