The mass of the sun is 1.99×10^30 kg and its distance to the Earth is 1.50×10^11 m. What is the gravitational force of the sun on the Earth, given that the mass of the Earth is 5.97×10^24 kg and the gravitational constant G is 6.674×10^-11 N(m/kg)^2?

• A. 1.23×10^21 N
• B. 2.98×10^25 N
• C. 3.54×10^22 N
• D. 4.36×10^20 N

Answer: (C)

Verified step by step guidance

1. Identify the formula for gravitational force, which is given by Newton's law of universal gravitation: $F=\frac{GmM}{r^2}$, where $F$ is the gravitational force, $G$ is the gravitational constant, $m$ and $M$ are the masses of the two objects, and $r$ is the distance between the centers of the two objects.
2. Substitute the given values into the formula: $F=\frac{6.674\times {10}^{-11}\times 5.97\times {10}^{24}\times 1.99\times {10}^{30}}{{1.50\times {10}^{11}}^2}$.
3. Calculate the numerator of the fraction, which involves multiplying the gravitational constant $G$, the mass of the Earth $m$, and the mass of the Sun $M$. This step involves handling large numbers and scientific notation.
4. Calculate the denominator, which is the square of the distance between the Earth and the Sun $r^2$. This involves squaring the given distance value.
5. Divide the calculated numerator by the calculated denominator to find the gravitational force $F$. This will give you the magnitude of the gravitational force exerted by the Sun on the Earth.