The asteroid Ceres has a mass 7.061 × 1020 kg
and a radius of 505.2 km.
What is g on the surface? The value
of the universal gravitational constant is
6.67259 × 10−11 N · m2/kg2.
To calculate the acceleration due to gravity (g) on the surface of an object, you can use the formula:
g = (G * M) / R^2
Where:
- G is the universal gravitational constant (6.67259 × 10^(-11) N·m^2/kg^2),
- M is the mass of the object (7.061 × 10^20 kg),
- R is the radius of the object (505.2 km or 505200 m).
Now, we can plug the given values into the formula and solve for g:
g = (6.67259 × 10^(-11) N·m^2/kg^2 * 7.061 × 10^20 kg) / (505200)^2 m^2
First, let's simplify the numerator:
Numerator = 6.67259 × 10^(-11) N·m^2/kg^2 * 7.061 × 10^20 kg
Using the product rule of exponents, we can add the powers of 10:
Numerator = (6.67259 * 7.061) × 10^(-11 + 20) N·m^2/kg^2
Numerator = 47.10843999 × 10^9 N·m^2/kg^2
Now, let's simplify the denominator:
Denominator = (505200)^2 m^2
Denominator = 255220400 m^2
Finally, we can substitute the values back into the formula and perform the calculation:
g = (47.10843999 × 10^9 N·m^2/kg^2) / 255220400 m^2
g ≈ 0.184 m/s^2
Therefore, the acceleration due to gravity on the surface of the asteroid Ceres is approximately 0.184 m/s^2.