https://file.aiquickdraw.com/mathbot/file/1730404783326yw3ne56r.jpg

The problem presented in the image provides several constants and asks to calculate the gravitational field strength. Here is a summary of the given dataThe problem presented in the image provides several constants and asks to calculate the gravitational field strength. Here is a summary of the given 

- Gravitational constant, \( G = 6.7 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \)
- Radius of Earth, \( R_{\text{Earth}} = 6.4 \times 10^6 \, \text{m} \)
- Mass of Earth, \( M_{\text{Earth}} = 6.0 \times 10^{24} \, \text{kg} \)
- Mass of the Sun, \( M_{\text{Sun}} = 2.0 \times 10^{30} \, \text{kg} \)
- Distance from Earth to the Sun, \( d_{\text{Earth-Sun}} = 1.5 \times 10^{11} \, \text{m} \)

### Solution
To calculate the gravitational field strength due to the Sun at Earth's location, we use the formula:

\[
g = \frac{GM_{\text{Sun}}}{d_{\text{Earth-Sun}}^2}
\]

Substitute the values:

1. \( G = 6.7 \times 10^{-11} \, \text{Nm}^2/\text{kg}^2 \)
2. \( M_{\text{Sun}} = 2.0 \times 10^{30} \, \text{kg} \)
3. \( d_{\text{Earth-Sun}} = 1.5 \times 10^{11} \, \text{m} \)

\[
g = \frac{(6.7 \times 10^{-11})(2.0 \times 10^{30})}{(1.5 \times 10^{11})^2}
\]

### Calculations

1. \( (1.5 \times 10^{11})^2 = 2.25 \times 10^{22} \, \text{m}^2 \)
2. \( (6.7 \times 10^{-11})(2.0 \times 10^{30}) = 1.34 \times 10^{20} \, \text{Nm}^2/\text{kg} \)

Thus,

\[
g = \frac{1.34 \times 10^{20}}{2.25 \times 10^{22}} = 5.96 \, \text{N/kg}
\]

### Answer:
The gravitational field strength due to the Sun at Earth's distance is approximately \( 5.96 \, \text{N/kg} \).

Would you like further details or explanations? 

Here are some related questions to explore this topic further:
1. What is the gravitational field strength on the surface of the Earth?
2. How does the gravitational force between Earth and the Sun compare to that between Earth and the Moon?
3. How would the gravitational field strength change if Earth were closer to the Sun?
4. What would happen to Earth's orbit if the mass of the Sun doubled?
5. How is gravitational field strength related to gravitational potential energy?

**Tip:** Gravitational field strength at a distance is inversely proportional to the square of the distance from the source mass.

Calculate the gravitational field strength at Earth's distance from the Sun, using provided constants.

Learn how to calculate the gravitational field strength due to the Sun at Earth's distance using Newton's Law of Gravitation. This problem covers gravitational field strength calculations with detailed steps and includes constants like Earth's mass, radius, and distance from the Sun.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation