Using newton's law of universal gravitation and the following data calculate the theoretical value of the acceleration due to gravity on mars.
Mars Mass= 6.4185x 10^23 kg
Radius (equatorial)= 3.3962x 10^6m
F=GMm/r^2
g=F/m=GM/r^2 put in M, r solve.
i got 3.71
is that right?
To calculate the theoretical value of the acceleration due to gravity on Mars using Newton's law of universal gravitation, we can use the following formula:
acceleration due to gravity = (G * mass of Mars) / (radius of Mars^2)
Where:
G is the gravitational constant = 6.67430 × 10^-11 m^3/(kg s^2)
Mass of Mars = 6.4185 × 10^23 kg
Radius of Mars = 3.3962 × 10^6 m
Plugging in these values into the formula, we get:
acceleration due to gravity on Mars = (6.67430 × 10^-11 m^3/(kg s^2) * 6.4185 × 10^23 kg) / (3.3962 × 10^6 m)^2
Now, let's calculate the value step-by-step:
Step 1: Calculate the square of the radius of Mars:
radius^2 = (3.3962 × 10^6 m)^2 = 1.1537 × 10^13 m^2
Step 2: Multiply the gravitational constant and the mass of Mars:
(6.67430 × 10^-11 m^3/(kg s^2)) * (6.4185 × 10^23 kg) = 4.2831 × 10^13 m^3/s^2
Step 3: Divide the result from step 2 by the result from step 1:
4.2831 × 10^13 m^3/s^2 / 1.1537 × 10^13 m^2 = 3.71 m/s^2
Therefore, the theoretical value of the acceleration due to gravity on Mars is approximately 3.71 m/s^2.