Determine the value for the acceleration due to gravity at the surface of the planet Mars, given the following data: Mass of Mars = 6 .42 x 10^23 kg Radius of Mars = 3.37 x 10^6 m
Thanks!
To determine the value for the acceleration due to gravity at the surface of Mars, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is directly proportional to their masses and inversely proportional to the square of the distance between their centers. Mathematically, it can be represented as:
F = (G * M * m) / r^2
Where:
F is the force of gravity
G is the gravitational constant (approximately 6.67430 × 10^-11 m^3 · kg^-1 · s^-2)
M is the mass of Mars
m is the mass of an object
r is the radius of Mars
The acceleration due to gravity at the surface of Mars can be obtained by dividing the gravitational force by the mass of the object. Since we want to determine the value for the acceleration, we can rewrite the equation as:
a = (G * M) / r^2
Now, plugging in the given values:
Mass of Mars (M) = 6.42 × 10^23 kg
Radius of Mars (r) = 3.37 × 10^6 m
We can calculate the value for the acceleration due to gravity on Mars using the given data and the formula mentioned above:
a = (6.67430 × 10^-11 m^3 · kg^-1 · s^-2 * 6.42 × 10^23 kg) / (3.37 × 10^6 m)^2
Simplifying the equation, we get:
a ≈ 3.69 m/s^2
Therefore, the acceleration due to gravity at the surface of Mars is approximately 3.69 m/s^2.
To determine the value for the acceleration due to gravity at the surface of Mars using the given data, we can use the equation for gravitational acceleration:
g = (G * M) / (r^2)
Where:
g is the acceleration due to gravity,
G is the gravitational constant (6.6743 x 10^(-11) N m^2 / kg^2),
M is the mass of Mars,
and r is the radius of Mars.
Plugging in the values:
M = 6.42 x 10^23 kg
r = 3.37 x 10^6 m
g = (6.6743 x 10^(-11) N m^2 / kg^2 * 6.42 x 10^23 kg) / (3.37 x 10^6 m)^2
Now, let's calculate the value for g step-by-step:
Step 1:
Multiply the gravitational constant by the mass of Mars:
= 6.6743 x 10^(-11) N m^2 / kg^2 * 6.42 x 10^23 kg
= 4.2866666 x 10^13 N m^2 / kg
Step 2:
Square the radius of Mars:
= (3.37 x 10^6 m)^2
= 1.13569 x 10^13 m^2
Step 3:
Divide the result from Step 1 by the result from Step 2:
= (4.2866666 x 10^13 N m^2 / kg) / (1.13569 x 10^13 m^2)
= 3.775848763 m/s^2
Therefore, the value for the acceleration due to gravity at the surface of Mars is approximately 3.78 m/s^2.