the diameter of the planet saturn is 10 times that of the earth but the mass of the planet is only 90 times greater than that of the earth.what is the gravitational acceleration or number gs you will feel on saturn?(8.8m.s-2)

F = m g = G M m/R^2

10 * R ---> 1/100
90 * m ----> 90

9.81 * 90/100 = 8.83 m/s^2

To calculate the gravitational acceleration (g) on Saturn, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

The equation is given by:

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

Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects (in this case, Earth and Saturn),
r is the distance between the centers of the two objects (in this case, the distance of a person from the center of Saturn).

We need to find g, the gravitational acceleration on Saturn. Gravitational acceleration is the acceleration due to gravity, which is the rate at which an object falls towards the center of an astronomical body.

To find g, we first need to find the mass of Saturn relative to that of Earth.

Given:
Diameter of Saturn = 10 times the diameter of Earth
Mass of Saturn = 90 times the mass of Earth

We know that the volume of a sphere is proportional to the cube of its diameter (assuming both spheres have the same material density). So, if the diameter of Saturn is 10 times that of Earth, then the volume of Saturn is (10^3) = 1000 times the volume of Earth.

Since the mass is directly proportional to the volume, the mass of Saturn is also 1000 times the mass of Earth.

Now, we can calculate the value of g on Saturn using the equation:

g = (G * Ms) / Rs^2

Where:
Ms is the mass of Saturn,
Rs is the radius of Saturn (since we need the distance from the center to the surface, not the diameter).

Since we know that the diameter of Saturn is 10 times that of Earth, we can calculate the radius of Saturn as:

Rs = (10 * Re) / 2

Where Re is the radius of Earth.

Now, we can substitute the values into the equation:

g = (G * (1000 * (mass of Earth))) / ((10 * (radius of Earth))^2)

Calculating the numerical value would yield:

g ≈ 8.8 m/s^2

So, the gravitational acceleration on Saturn is approximately 8.8 m/s^2, which is the same as the given value.