Compute the surface gravity, g, for the surface of Mercury. Its radius is 2.4 x 10^6 m and its mass is 3.3 x 10^23 kg
Question
Compute the surface gravity, g, for the surface of Mercury. Its radius is 2.4 x 10^6 m and its mass is 3.3 x 10^23 kg
Solution
Sure, to compute the surface gravity of a planet, we can use the formula for gravitational force:
g = GM/r^2
where:
- G is the gravitational constant, approximately 6.674 x 10^-11 N(m/kg)^2,
- M is the mass of the planet, and
- r is the radius of the planet.
Substituting the given values:
g = (6.674 x 10^-11 N(m/kg)^2 * 3.3 x 10^23 kg) / (2.4 x 10^6 m)^2
First, calculate the numerator:
= 2.202 x 10^13 Nm^2/kg
Then, calculate the denominator:
= (2.4 x 10^6 m)^2 = 5.76 x 10^12 m^2
Finally, divide the numerator by the denominator:
g = 2.202 x 10^13 Nm^2/kg / 5.76 x 10^12 m^2 = 3.82 m/s^2
So, the surface gravity on Mercury is approximately 3.82 m/s^2.
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