The acceleration due to gravity at Earth's surface is 9.80 m/s2. What is the acceleration at altitudes of 100 km?
The acceleration due to gravity at Earth's surface is 9.80 m/s2. What is the acceleration at altitudes of 100 km?
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![**Acceleration Due to Gravity at Different Altitudes**
The acceleration due to gravity at Earth’s surface is \(9.80 \, \text{m/s}^2\). What is the acceleration at an altitude of 100 km?
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**Explanation:**
When an object is at the surface of the Earth, it experiences gravitational acceleration of \(9.80 \, \text{m/s}^2\). However, as we move away from the Earth's surface, the gravitational acceleration decreases with the square of the distance from the center of the Earth. This relationship is described by the formula:
\[ g = \frac{GM}{(R+h)^2} \]
Where:
- \( G \) is the gravitational constant \((6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2) \),
- \( M \) is the mass of the Earth \((5.98 \times 10^{24} \, \text{kg})\),
- \( R \) is the radius of the Earth \((6.371 \times 10^6 \, \text{m})\),
- \( h \) is the altitude above the Earth's surface (100 km or 100,000 m in this case).
By substituting these values into the formula, one can calculate the acceleration due to gravity at 100 km altitude.
Note: Please include a derivation of this formula and the calculation steps in the actual course content for better comprehension.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe8677b-d2b4-4cf1-b1ed-08820154fcb5%2F8cbc3e3a-1fe8-42e1-8f42-fb0b7d33e0c8%2Fbh3wct9_processed.png&w=3840&q=75)
Transcribed Image Text:**Acceleration Due to Gravity at Different Altitudes**
The acceleration due to gravity at Earth’s surface is \(9.80 \, \text{m/s}^2\). What is the acceleration at an altitude of 100 km?
---
**Explanation:**
When an object is at the surface of the Earth, it experiences gravitational acceleration of \(9.80 \, \text{m/s}^2\). However, as we move away from the Earth's surface, the gravitational acceleration decreases with the square of the distance from the center of the Earth. This relationship is described by the formula:
\[ g = \frac{GM}{(R+h)^2} \]
Where:
- \( G \) is the gravitational constant \((6.674 \times 10^{-11} \, \text{N} \cdot \text{m}^2/\text{kg}^2) \),
- \( M \) is the mass of the Earth \((5.98 \times 10^{24} \, \text{kg})\),
- \( R \) is the radius of the Earth \((6.371 \times 10^6 \, \text{m})\),
- \( h \) is the altitude above the Earth's surface (100 km or 100,000 m in this case).
By substituting these values into the formula, one can calculate the acceleration due to gravity at 100 km altitude.
Note: Please include a derivation of this formula and the calculation steps in the actual course content for better comprehension.
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