(a) The mass of Venus \(\displaystyle{M}_{{{V}}}\) represent 81.5% of the of the Earth. So, the mass of Venus is

\(\displaystyle{M}_{{{V}}}\)=(81.5%)\(\displaystyle{M}_{{{E}}}\)

(1)

Where \(\displaystyle{M}_{{{E}}}\) is the mass of the Earth. Plug the mass of Earth into equation (1), so we can get \(\displaystyle{M}_{{{V}}}\) by

\(\displaystyle{M}_{{{V}}}={\left({0.815}\right)}{M}_{{{E}}}={\left({0.815}\right)}{\left({5.97}\times{10}^{{{24}}}{k}{g}\right)}={4.86}\times{10}^{{{24}}}{k}{g}\)

The radius of Venus represent 94.9% of the radius of the Earth. So, the radius of Venus is

\(\displaystyle{R}_{{{V}}}={\left({94.9}\%\right)}{R}_{{{E}}}\)

(2)

Where \(\displaystyle{R}_{{{E}}}\) is the radius of the Earth. Plug the radius of Earth into equation (2), so we can get \(\displaystyle{R}_{{{V}}}\) by

\(\displaystyle{R}_{{{V}}}={\left({0.949}\right)}{\left({6.38}\times{10}^{{{6}}}{m}\right)}={6.05}\times{10}^{{{6}}}{m}\)

The weight w of a body is the total gravitational force exerted on it by all other bodies in the univerce where this gravitational force F is given by Newton`s general law of gravity by

\(\displaystyle{F}={G}{\frac{{{M}_{{{V}}}{m}}}{{{{R}_{{V}}^{{2}}}}}}\)

(3)

Where \(\displaystyle{R}_{{{V}}}\) is the radius of Venus, m is the mass of the body. As we mentioned above, this gravitational force equals the weight of the body which is mg, so using equation (3) we get the acceleration on Venus by

\(\displaystyle{m}{g}={G}{\frac{{{M}_{{{V}}}{m}}}{{{{R}_{{V}}^{{2}}}}}}\)

\(\displaystyle{g}{v}={G}{\frac{{{M}_{{{V}}}}}{{{{R}_{{V}}^{{2}}}}}}\)

(4)

Now, we plug values for \(\displaystyle{R}_{{{V}}}\), \(\displaystyle{M}_{{{V}}}\) and G into equation (4) to get gv

\(\displaystyle{g}{v}={\frac{{{G}{M}_{{{V}}}}}{{{{R}_{{V}}^{{2}}}}}}\)

\(\displaystyle={\frac{{{\left({6.67}\times{10}^{{-{11}}}{N}\cdot{m}^{{{2}}}\div{k}{g}^{{{2}}}\right)}{\left({4.86}\times{10}^{{{24}}}{k}{g}\right)}}}{{{\left({6.05}\times{10}^{{{6}}}{m}\right)}^{{{2}}}}}}\)

\(\displaystyle={8.86}{m}\div{s}^{{{2}}}\)

\(\displaystyle{M}_{{{V}}}\)=(81.5%)\(\displaystyle{M}_{{{E}}}\)

(1)

Where \(\displaystyle{M}_{{{E}}}\) is the mass of the Earth. Plug the mass of Earth into equation (1), so we can get \(\displaystyle{M}_{{{V}}}\) by

\(\displaystyle{M}_{{{V}}}={\left({0.815}\right)}{M}_{{{E}}}={\left({0.815}\right)}{\left({5.97}\times{10}^{{{24}}}{k}{g}\right)}={4.86}\times{10}^{{{24}}}{k}{g}\)

The radius of Venus represent 94.9% of the radius of the Earth. So, the radius of Venus is

\(\displaystyle{R}_{{{V}}}={\left({94.9}\%\right)}{R}_{{{E}}}\)

(2)

Where \(\displaystyle{R}_{{{E}}}\) is the radius of the Earth. Plug the radius of Earth into equation (2), so we can get \(\displaystyle{R}_{{{V}}}\) by

\(\displaystyle{R}_{{{V}}}={\left({0.949}\right)}{\left({6.38}\times{10}^{{{6}}}{m}\right)}={6.05}\times{10}^{{{6}}}{m}\)

The weight w of a body is the total gravitational force exerted on it by all other bodies in the univerce where this gravitational force F is given by Newton`s general law of gravity by

\(\displaystyle{F}={G}{\frac{{{M}_{{{V}}}{m}}}{{{{R}_{{V}}^{{2}}}}}}\)

(3)

Where \(\displaystyle{R}_{{{V}}}\) is the radius of Venus, m is the mass of the body. As we mentioned above, this gravitational force equals the weight of the body which is mg, so using equation (3) we get the acceleration on Venus by

\(\displaystyle{m}{g}={G}{\frac{{{M}_{{{V}}}{m}}}{{{{R}_{{V}}^{{2}}}}}}\)

\(\displaystyle{g}{v}={G}{\frac{{{M}_{{{V}}}}}{{{{R}_{{V}}^{{2}}}}}}\)

(4)

Now, we plug values for \(\displaystyle{R}_{{{V}}}\), \(\displaystyle{M}_{{{V}}}\) and G into equation (4) to get gv

\(\displaystyle{g}{v}={\frac{{{G}{M}_{{{V}}}}}{{{{R}_{{V}}^{{2}}}}}}\)

\(\displaystyle={\frac{{{\left({6.67}\times{10}^{{-{11}}}{N}\cdot{m}^{{{2}}}\div{k}{g}^{{{2}}}\right)}{\left({4.86}\times{10}^{{{24}}}{k}{g}\right)}}}{{{\left({6.05}\times{10}^{{{6}}}{m}\right)}^{{{2}}}}}}\)

\(\displaystyle={8.86}{m}\div{s}^{{{2}}}\)