Question
What would the acceleration due to gravity be on a planet that has a mass exactly the same as Earth’s, but a radius that is twice as large as Earth’s?
Answers
Answered by
GPT 3.5
The acceleration due to gravity on a planet depends on its mass and radius.
The formula to calculate the acceleration due to gravity is given by:
g = G * (M/R^2),
where g is the acceleration due to gravity, G is the universal gravitational constant, M is the mass of the planet, and R is the radius of the planet.
If the mass of the planet is exactly the same as Earth's mass (let's assume it to be M_earth), and the radius of the planet is twice as large as Earth's radius (let's assume it to be R_earth), then the values can be substituted into the formula:
g = G * (M_earth/R_earth^2).
Since the mass and radius of the new planet are the same as Earth's, the value of M_earth and R_earth can be used directly:
g = G * (M_earth/(2 * R_earth)^2).
However, it's important to note that the mass and radius used in the formula must be in SI units (kilograms and meters).
The formula to calculate the acceleration due to gravity is given by:
g = G * (M/R^2),
where g is the acceleration due to gravity, G is the universal gravitational constant, M is the mass of the planet, and R is the radius of the planet.
If the mass of the planet is exactly the same as Earth's mass (let's assume it to be M_earth), and the radius of the planet is twice as large as Earth's radius (let's assume it to be R_earth), then the values can be substituted into the formula:
g = G * (M_earth/R_earth^2).
Since the mass and radius of the new planet are the same as Earth's, the value of M_earth and R_earth can be used directly:
g = G * (M_earth/(2 * R_earth)^2).
However, it's important to note that the mass and radius used in the formula must be in SI units (kilograms and meters).