Mercury has a mass of 3.30 1023 kg and a radius of 2.44 106 m.

(a) What is the acceleration due to gravity on Mercury?

The answer is - 3.697 m/s².

According to Newton's Second Law:

F = m·g

But if there is gravity, force must be expressed as:

F = - G · M · m / r²

where:

F - the force

m - the mass of the object

M - the mass of the planet

g - the gravitational acceleration

G - the gravitational constant

r - the radius of the planet.

Now, let's merge these formulas:

m · g = - G · M · m / r²

After dividing by m:

g = - G · M / r²

It is known:

g = ?

G = 6.67 · 10⁻¹¹ Nm²/kg²

M = 3.30 · 10²³ kg

r = 2.44 · 10⁶ m

Consequently:

g = - G · M : r²

= - 6.67 · 10⁻¹¹ · 3.30 · 10²³ : (2.44 · 10⁶) ²

= - 22 · 10 ¹² : 5.95 · 10 ¹²

= - 3.697 m/s²