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?
To compare the gravity on two planets, we can use the formula for gravitational acceleration, which is given by:
g = (G * M) / (r^2)
where:
- g is the gravitational acceleration
- G is the gravitational constant
- M is the mass of the planet
- r is the radius of the planet
In this case, it is mentioned that Planet X has the same mass as Earth but its radius is only half as big. Let's denote the gravitational acceleration on Earth as 'g_earth' and on Planet X as 'g_x'.
Using the formula above, we can write the following equations for Earth and Planet X:
g_earth = (G * M_earth) / (r_earth^2)
g_x = (G * M_x) / (r_x^2)
Given that both planets have the same mass, we can write: M_earth = M_x = M (let's denote it as 'M' for simplicity).
For the radius, it is mentioned that the radius of Planet X is only half as big compared to Earth. So we have: r_x = 0.5 * r_earth.
Substituting these values into the equations, we get:
g_earth = (G * M) / (r_earth^2)
g_x = (G * M) / (r_x^2) = (G * M) / ((0.5 * r_earth)^2)
= (G * M) / (0.25 * r_earth^2)
= 4 * (G * M) / (r_earth^2)
Now we can compare the two gravitational accelerations, g_earth and g_x:
g_x / g_earth = (4 * (G * M) / (r_earth^2)) / ((G * M) / (r_earth^2))
= 4
So, the gravity on Planet X would be four times stronger than the gravity on Earth.
Hint: g at the surface is proportional to M/R^2.
M is the same for each.
Note the correct spelling of the subject