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

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.