Answer:
The radius of the new planet is ~2.04 * 10⁶ m, or 2,041,752 m.
Explanation:
We can use Newton's Law of Universal Gravitation:
- [tex]\displaystyle F_g=G\frac{Mm}{r^2}[/tex]
Let's look at Newton's 2nd Law:
We can set these equations equal to each other:
- [tex]\displaystyle G\frac{Mm}{r^2} =ma[/tex]
The mass of the second mass (astronaut) cancels out. We are left with:
- [tex]\displaystyle G\frac{M}{r^2} =a[/tex]
We are solving for the radius of the new planet, so we can rearrange the equation:
- [tex]\displaystyle r=\sqrt{\frac{GM}{a} }[/tex]
Substitute in our known values given in the problem (G = 6.67 * 10⁻¹¹ ; M = 7.5 * 10²³ ; a = 12).
- [tex]\displaystyle r =\sqrt{\frac{(6.67\times 10^{-11})(7.5 \times 10^{23}}{12} }[/tex]
- [tex]r=2.04 \times 10^6[/tex]
The radius of the new planet is ~2.04 * 10⁶ m.
