Question

Calculate the gravitational force of the sun on mars if the distance between these two celestial bodies are approximately 143.82 million miles apart (assume this is from center to center). The given mass of the sun is 1.99x10^30 kg, the given mass of mars is 6.42x10^23 kg. The given radius of the sun is 6.96x10^8 m and the given radius of mars is 3.40x10^6 m.

Answer 1

1.6 x 10^21 N

Step-by-step explanation:

The gravitational force can be calculated as

`F=G(M_1\cdot M_2)/(r^2)`

Where G = 6.674 x 10^(-11) m³/kg s². M1 and M2 are the mass and r is the distance between the objects. So, first, we need to convert 143.82 million miles to meters as

`143.82*10^6\text{ miles}*\frac{1609\text{ m}}{1\text{ mile}}=2.31*10^(11)m`

Then, we can replace M1 = 1.99 x 10^30 kg, M2 = 6.42 x 10^23 kg, and r = 2.31 x 10^11 m to get

`\begin{gathered} F=(6.674*10^(-11))((1.99*10^(30))(6.42*10^(23)))/((2.31*10^(11))) \\ \\ F=1.6*10^(21)\text{ N} \end{gathered}`

Therefore, the gravitational force is 1.6 x 10^21 N