Question regarding calculating acceleration due to gravity on planet Mercury I was asked to calcul

syaoronsangelhwc17 2022-05-10 Answered

Question regarding calculating acceleration due to gravity on planet Mercury
I was asked to calculate the acceleration due to gravity on planet Mercury, if the mas of Mercury is

2, 99 \times 10^{22} k g

and its radius is

2, 42 \times 10^{3} k m

. The mass of the object is

10 k g

and the mass of Earth is

6 \times 10^{24} k g

and the Radius of the Earth is

3, 82 \times 10^{3} k m

This question rather puzzled me because I was not sure if my answer is correct or not but let me proceed :

\vec{F} = m \vec{a} = F_{g} = G \frac{m_{1} m_{2}}{r^{2}}

m_{1} g = G \frac{m_{1} m_{2}}{r^{2}}

(Note that

m_{2}

= mass of mercury)

g = \frac{(6.673 \times 10^{- 11} \frac{m^{2}}{k g^{2}}) (2, 99 \times 10^{22} k g)}{(2, 42 \times 10^{6} m)^{2}}

I compute my answer to be

0.34 \frac{m}{s^{2}}

What really is confusing me is that when I look at my textbook, it shows me the gravitational acceleration due to gravity on mercury to be

3.59 \frac{m}{s^{2}}

Can someone please explain to me what the answer that I am getting is giving me? My computation was marked correct in a test but I do not understand what this value is giving me.

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Answers (1)

odvucimo1pp17

Answered 2022-05-11 Author has 23 answers

That value for the mass of Mercury is not correct.
The correct value is

3.3 \times 10^{23}

kg.

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