6. the sun has a mass of 2 x 10^{30}. if the gravitational force between it and another planet that is 4.1 x 10^{14} m away is 5.2 x 10^{18} n, what is the mass of the planet?

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Accepted Answer

# Explanation:
## Step1: Recall the gravitational force formula
The formula for gravitational force is $F = G\frac{m_1m_2}{r^2}$, where $F$ is the gravitational force, $G = 6.67\times10^{- 11}\text{ N}\cdot\text{m}^2/\text{kg}^2$ (universal gravitational constant), $m_1$ and $m_2$ are the masses of the two objects, and $r$ is the distance between them. We need to solve for $m_2$. Rearranging the formula for $m_2$ gives $m_2=\frac{F\times r^2}{G\times m_1}$.
## Step2: Substitute the given values
We are given that $F = 5.2\times10^{18}\text{ N}$, $m_1 = 2\times10^{30}\text{ kg}$, $r = 4.1\times10^{14}\text{ m}$, and $G = 6.67\times10^{-11}\text{ N}\cdot\text{m}^2/\text{kg}^2$.
Substitute these values into the formula:
$$
\begin{align*}
m_2&=\frac{(5.2\times 10^{18})\times(4.1\times 10^{14})^2}{(6.67\times 10^{-11})\times(2\times 10^{30})}\
&=\frac{5.2\times10^{18}\times16.81\times10^{28}}{13.34\times10^{-11 + 30}}\
&=\frac{87.412\times10^{46}}{13.34\times10^{19}}\
&=\frac{87.412}{13.34}\times10^{46-19}\
&\approx6.55\times10^{27}\text{ kg}
\end{align*}
$$

# Answer:
The mass of the planet is approximately $6.55\times 10^{27}\text{ kg}$

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Question

Explanation:

Step1: Recall the gravitational force formula

Step2: Substitute the given values

Answer: