The Gravitational Force Between The Sun (mass $1.99 \times 10^{30} , \text{kg}$) And Mercury (mass $3.30 \times 10^{23} , \text{kg}$) Is $ 8.99 × 10 21 N 8.99 \times 10^{21} \, \text{N} 8.99 × 1 0 21 N [/tex]. How Far Is Mercury From The Sun?A.
**The Gravitational Force Between the Sun and Mercury: Understanding the Distance** ===========================================================
Introduction
The gravitational force between two celestial bodies is a fundamental concept in physics that helps us understand the behavior of objects in our universe. In this article, we will explore the gravitational force between the Sun and Mercury, and use it to calculate the distance between these two celestial bodies.
What is Gravitational Force?
Gravitational force is a force that attracts two objects with mass towards each other. It is a universal force that affects everything with mass, from the smallest subatomic particles to the largest galaxies. The strength of the gravitational force depends on the mass of the objects and the distance between them.
The Gravitational Force Formula
The gravitational force between two objects can be calculated using the following formula:
F = G * (m1 * m2) / r^2
Where:
- F is the gravitational force between the two objects
- G is the gravitational constant (6.674 * 10^-11 N m^2 kg^-2)
- m1 and m2 are the masses of the two objects
- r is the distance between the two objects
Calculating the Distance Between the Sun and Mercury
Now that we have the formula for gravitational force, we can use it to calculate the distance between the Sun and Mercury. We are given the following values:
- The mass of the Sun is 1.99 * 10^30 kg
- The mass of Mercury is 3.30 * 10^23 kg
- The gravitational force between the Sun and Mercury is 8.99 * 10^21 N
We can plug these values into the formula for gravitational force and solve for r:
F = G * (m1 * m2) / r^2 8.99 * 10^21 = (6.674 * 10^-11) * (1.99 * 10^30) * (3.30 * 10^23) / r^2
Simplifying the equation, we get:
r^2 = (6.674 * 10^-11) * (1.99 * 10^30) * (3.30 * 10^23) / (8.99 * 10^21) r^2 = 5.79 * 10^14 r = sqrt(5.79 * 10^14) r = 7.64 * 10^7 km
Therefore, the distance between the Sun and Mercury is approximately 76.4 million kilometers.
Q&A
Q: What is the gravitational force between the Sun and Mercury? A: The gravitational force between the Sun and Mercury is 8.99 * 10^21 N.
Q: What is the mass of the Sun? A: The mass of the Sun is 1.99 * 10^30 kg.
Q: What is the mass of Mercury? A: The mass of Mercury is 3.30 * 10^23 kg.
Q: How far is Mercury from the Sun? A: Mercury is approximately 76.4 million kilometers from the Sun.
Q: What is the gravitational constant? A: The gravitational constant is 6.674 * 10^-11 N m^2 kg^-2.
Conclusion
In this article, we used the formula for gravitational force to calculate the distance between the Sun and Mercury. We found that the distance between these two celestial bodies is approximately 76.4 million kilometers. This calculation demonstrates the power of physics in understanding the behavior of objects in our universe.
Further Reading
For more information on gravitational force and its applications, please see the following resources: