Question

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?

Explanation:

Step1: Write the formula for gravitational force

The formula for gravitational force is \(F = G\frac{Mm}{r^{2}}\), where \(F\) is the gravitational force, \(G = 6.67\times10^{- 11}\space Nm^{2}/kg^{2}\) (universal gravitational constant), \(M\) is the mass of the sun, \(m\) is the mass of the planet, and \(r\) is the distance between them.
We need to solve for \(m\), so we can re - arrange the formula to \(m=\frac{F\times r^{2}}{G\times M}\)

Step2: Substitute the given values

Given \(F = 5.2\times10^{18}\space N\), \(M = 2\times10^{30}\space kg\), \(r = 4.1\times10^{14}\space m\), and \(G = 6.67\times10^{-11}\space Nm^{2}/kg^{2}\)

Substitute these values into the formula:

$$
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$$

Step3: Calculate the value

\(\frac{87.412}{13.34}\approx6.55\)

\(m\approx6.55\times10^{27}\space kg\)

Answer:

The mass of the planet is approximately \(6.55\times 10^{27}\space kg\)