Question

An astronaut lands on a new, recently discovered planet in a different star system. The astronaut measures the acceleration due to gravity on the planet to be 12m/s2, and the mass of the planet is measured to be 7. 5E23kg. What is the radius of the new planet?

Answer 1

The radius of the new planet is ~2.04 * 10⁶ m, or 2,041,752 m.

Step-by-step explanation:

We can use Newton's Law of Universal Gravitation:

• 
  `\displaystyle F_g=G(Mm)/(r^2)`

Let's look at Newton's 2nd Law:

• 
  `F=ma`

We can set these equations equal to each other:

• 
  `\displaystyle G(Mm)/(r^2) =ma`

The mass of the second mass (astronaut) cancels out. We are left with:

• 
  `\displaystyle G(M)/(r^2) =a`

We are solving for the radius of the new planet, so we can rearrange the equation:

• 
  `\displaystyle r=\sqrt{(GM)/(a) }`

Substitute in our known values given in the problem (G = 6.67 * 10⁻¹¹ ; M = 7.5 * 10²³ ; a = 12).

• 
  `\displaystyle r =\sqrt{((6.67* 10^(-11))(7.5 * 10^(23))/(12) }`
• 
  `r=2.04 * 10^6`

The radius of the new planet is ~2.04 * 10⁶ m.