Planet X has the same mass as earth, but its radius is only half as big. How does the gravity on this planet compare with the gravity on our planet earth?

g1 = G•M/R^2

g2 = G•M/r^2
r=R/2
g1/g2=r^2/R^2=1/4

The gravitational force experienced by an object depends on two factors: the mass of the object and the distance between the object and the source of gravity. In the case of Planet X, it has the same mass as Earth but a smaller radius.

To compare the gravity on Planet X with Earth, we can use the formula for gravitational force:

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

Where:
F is the gravitational force between the two objects,
G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects,
r is the distance between the centers of the two objects.

Since the mass of Planet X is the same as Earth, m1 = m2. The only difference is the radius, so we can compare the effects of radius (r) on gravity.

Let's assume that the radius of Earth is rE and the radius of Planet X is rX. Given that rX is half the value of rE (rX = 0.5 * rE), we can substitute these values into the formula to compare the gravitational forces:

FE = G * (m1 * m2) / rE^2
FX = G * (m1 * m2) / rX^2

Dividing the second equation by the first equation, we get:

FX / FE = (G * (m1 * m2) / rX^2) / (G * (m1 * m2) / rE^2)
= (rE^2 / rX^2)

Substituting the values rX = 0.5 * rE and simplifying the equation, we find:

FX / FE = (rE^2 / (0.5 * rE)^2)
= (4 * rE^2 / rE^2)
= 4

Therefore, the gravity on Planet X is 4 times stronger than the gravity on Earth.

To compare the gravity on Planet X with that on Earth, we can use the equation for gravitational force, Newton's Law of Universal Gravitation:

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

Where:
F = gravitational force
G = gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2)
m1, m2 = masses of the two objects
r = distance between the centers of the two objects

In this case, the mass of Planet X is the same as Earth, but the radius is half as big. Let's assume the mass of both Planet X and Earth is "m" and the radius of Earth is "r".

Planet X:
Mass (m1) = m
Radius (r1) = 0.5r

Earth:
Mass (m2) = m
Radius (r2) = r

To compare the gravity, let's calculate the ratio of the gravitational forces between Planet X and Earth using the equation above:

F1/F2 = (G * m1 * m2) / (r1^2) / (G * m1 * m2) / (r2^2)
= (r2^2) / (r1^2)
= (r^2) / (0.5r)^2
= r^2 / (0.25r^2)
= 4

Therefore, the ratio of the gravitational forces is 4, meaning the gravity on Planet X is four times stronger than that on Earth. In other words, if you were on Planet X, you would experience an acceleration due to gravity four times stronger than on Earth.

Duplicate question. Refer to my response elsewhere.