If the mass of a planet is 0.571 times that of the Earth and its radius is 0.787 times that of the Earth, estimate the gravitational field g at the surface of the planet. The gravitational acceleration on Earth is 9.8 m/s2.
Answer in units of m/s2
For earth, g = GMm/r^2 = 9.8
For planet x, we have
GM(.571m)/(.787r)^2 = GMm/r^2 * .571/.787^2 = .922g = ?
To estimate the gravitational field at the surface of the planet, we can use the formula for gravitational field strength:
g = (G * M) / r^2
Where:
- g is the gravitational field strength
- G is the gravitational constant (approximately 6.67 * 10^-11 N m^2/kg^2)
- M is the mass of the planet
- r is the radius of the planet
Given that the mass of the planet is 0.571 times that of the Earth and its radius is 0.787 times that of the Earth, we can substitute these values into the formula.
Let's start by finding the mass of the planet relative to Earth's mass:
M = 0.571 * (mass of Earth)
Next, we can find the radius of the planet relative to Earth's radius:
r = 0.787 * (radius of Earth)
Now, substitute these values into the formula for gravitational field strength:
g = (6.67 * 10^-11 N m^2/kg^2 * 0.571 * (mass of Earth)) / (0.787 * (radius of Earth)^2)
Since we know that the gravitational acceleration on Earth is 9.8 m/s^2, we can divide the above equation by 9.8 to get the answer in units of m/s^2.
g = ((6.67 * 10^-11 N m^2/kg^2 * 0.571 * (mass of Earth)) / (0.787 * (radius of Earth)^2)) / 9.8
Now, plug in the actual values for the mass of Earth and the radius of Earth, and calculate the result to estimate the gravitational field strength on the surface of the planet.