Answer: 28
Explanation:
According to Newton's law of Gravitation the gravitational force on the surface of the Sun [tex]Fg_{s}[/tex] is:
[tex]Fg_{s}=mg_{sun}=G\frac{Mm}{r^{2}}[/tex] (1)
Where:
[tex]m[/tex] is your mass
[tex]g_{sun}[/tex] is the acceleration due gravity on the surface of the Sun
[tex]G=6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}[/tex] is the gravitational constant
[tex]M=1.99(10)^{30} kg[/tex] is the mass of the Sun
[tex]r=6.96(10)^{8} m[/tex] is the radius of the Sun
Simplifying:
[tex]g_{sun}=G\frac{M}{r^{2}}[/tex] (2)
[tex]g_{sun}=6.674(10)^{-11} \frac{m^{3}}{kgs^{2}} \frac{1.99(10)^{30} kg}{(6.96(10)^{8} m)^{2}}[/tex] (3)
[tex]g_{sun}=274 m/s^{2}[/tex] (4)
Since the acceleration due gravity on Earth is [tex]g_{E}=9.8 m/s^{2}[/tex], the relation is:
[tex]\frac{g_{sun}}{g_{E}}=\frac{274 m/s^{2}}{9.8 m/s^{2}}[/tex]
[tex]\frac{g_{sun}}{g_{E}}=27.9 \approx 28[/tex]
Hence, your weight would increase by a factor of 28.
