Answer:
R = 7.02 × 10^6 meters
Step-by-step explanation:
To calculate the value of acceleration due to gravity at the surface of a heavenly body with a given value, we can use the formula:
g = G*M/R^2
Where:
g = acceleration due to gravity at the surface
G = gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
M = mass of the heavenly body
R = radius of the heavenly body
Substituting the given value of acceleration due to gravity (g = 2.25 m/s^2) and assuming that the mass of the heavenly body is known (let's say M = 6.0 × 10^24 kg), we can rearrange the formula to solve for the radius R:
R = sqrt(G*M/g)
Plugging in the values, we get:
R = sqrt((6.67430 × 10^-11 m^3 kg^-1 s^-2) * (6.0 × 10^24 kg) / (2.25 m/s^2))
Simplifying the expression, we get:
R = 7.02 × 10^6 meters
Therefore, the radius of the heavenly body would be approximately 7.02 × 10^6 meters, assuming a mass of 6.0 × 10^24 kg and an acceleration due to gravity at the surface of 2.25 m/s^2.
Note that this is a hypothetical scenario as the value of acceleration due to gravity varies from planet to planet and other celestial bodies.