The kepler mission has recently discovered a number of rocky planets around the stars.Suppose one of these planets has a mass of 7.66 x 10^24 kg and radius of 6743 km.What is the acceleration due to gravity(that is gravitational field) on the surface of the exoplanet?
g = F/m = G M/r^2
where
G = 6.67*10^-11
M = 7.66*10^24
r = 6.74*10^6
11.2 m/s^2
as compared to 9.81 on earth
To find the acceleration due to gravity on the surface of a planet, we can use the following formula:
acceleration due to gravity (g) = (G * M) / R^2
where:
- G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 kg^-1 s^-2)
- M is the mass of the planet
- R is the radius of the planet
First, let's convert the given values to the appropriate units:
- Mass (M) = 7.66 x 10^24 kg
- Radius (R) = 6743 km = 6743 x 10^3 m
Now, let's calculate the acceleration due to gravity:
g = (6.67430 × 10^-11 * 7.66 x 10^24) / (6743 x 10^3)^2
Simplifying the equation:
g = (6.67430 × 10^-11 * 7.66 x 10^24) / (6743)^2 * (10^3)^2
g = (4.82176478 × 10^13) / 45561249 * (10^6)
g = 4.82176478 × 10^13 / 45561249 × 10^6
g ≈ 105.88 m/s^2
Therefore, the acceleration due to gravity on the surface of the exoplanet is approximately 105.88 m/s^2.