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 · 10¹² ÷ 5.95 · 10 ¹²
   = - 3.697 m/s²

Hey hope you get the answer but i suck at math sorry : (

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