A planet/moon has a mass of 77.89 × 1023 kg and a radius of 7.9 × 106 meters. What is g on the surface to the nearest hundredth of a m/s2?
Once again, not really sure where to go with this. Out of the 10 problems I've only had trouble with this and one other.
the gravitational constant
G =6.67•10⁻¹¹ N•m²/kg²,
mg =GmM/R²,
g =G M/R²=
=6.67•10⁻¹¹•77.89•10²³/(7.9•10⁶)²=
=8.32 m/s²
To find the acceleration due to gravity (g) on the surface of a planet or moon, we can use the formula:
g = G * (M / R^2)
where:
- g is the acceleration due to gravity
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3/kg/s^2)
- M is the mass of the planet/moon
- R is the radius of the planet/moon
Let's plug in the values given in the problem:
M = 77.89 × 10^23 kg
R = 7.9 × 10^6 meters
Now we can calculate g:
g = (6.67430 × 10^-11 m^3/kg/s^2) * (77.89 × 10^23 kg) / (7.9 × 10^6 meters)^2
Step 1: Calculate the value in the numerator:
(6.67430 × 10^-11 m^3/kg/s^2) * (77.89 × 10^23 kg) = 5.19538 × 10^13 kg*m^3/s^2
Step 2: Calculate the value in the denominator:
(7.9 × 10^6 meters)^2 = 6.241 × 10^13 meters^2
Step 3: Calculate g:
g = 5.19538 × 10^13 kg*m^3/s^2 / 6.241 × 10^13 meters^2
Divide these values to get the value of g.