What is the acceleration due to gravity at an altitude of 1000 km.
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![**Question**: What is the acceleration due to gravity at an altitude of 1000 km?
**Answer**: To calculate the acceleration due to gravity at an altitude (h) of 1000 km above the Earth's surface, we can use the following formula:
\[ g_h = \frac{g_0 R^2}{(R + h)^2} \]
where:
- \( g_h \) is the acceleration due to gravity at height \( h \) above the Earth's surface.
- \( g_0 \) is the standard acceleration due to gravity at the Earth's surface (approximately 9.81 m/s²).
- \( R \) is the radius of the Earth (approximately 6,371 km).
- \( h \) is the height above the Earth's surface (1000 km in this case).
First, convert all measurements to meters:
- \( R = 6,371 \, km = 6,371,000 \, m \)
- \( h = 1,000 \, km = 1,000,000 \, m \)
Substitute into the formula:
\[ g_h = \frac{9.81 \times (6,371,000)^2}{(7,371,000)^2} \]
Calculate the terms in the formula:
\[ g_h = \frac{9.81 \times 40,611,241,000,000}{54,348,641,000,000} \]
\[ g_h \approx 7.33 \, m/s^2 \]
Therefore, the acceleration due to gravity at an altitude of 1000 km is approximately 7.33 m/s².](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3fe8677b-d2b4-4cf1-b1ed-08820154fcb5%2F55269f40-ec9b-4963-9df8-655e1e4e38a4%2Fvzondy_processed.png&w=3840&q=75)
Transcribed Image Text:**Question**: What is the acceleration due to gravity at an altitude of 1000 km?
**Answer**: To calculate the acceleration due to gravity at an altitude (h) of 1000 km above the Earth's surface, we can use the following formula:
\[ g_h = \frac{g_0 R^2}{(R + h)^2} \]
where:
- \( g_h \) is the acceleration due to gravity at height \( h \) above the Earth's surface.
- \( g_0 \) is the standard acceleration due to gravity at the Earth's surface (approximately 9.81 m/s²).
- \( R \) is the radius of the Earth (approximately 6,371 km).
- \( h \) is the height above the Earth's surface (1000 km in this case).
First, convert all measurements to meters:
- \( R = 6,371 \, km = 6,371,000 \, m \)
- \( h = 1,000 \, km = 1,000,000 \, m \)
Substitute into the formula:
\[ g_h = \frac{9.81 \times (6,371,000)^2}{(7,371,000)^2} \]
Calculate the terms in the formula:
\[ g_h = \frac{9.81 \times 40,611,241,000,000}{54,348,641,000,000} \]
\[ g_h \approx 7.33 \, m/s^2 \]
Therefore, the acceleration due to gravity at an altitude of 1000 km is approximately 7.33 m/s².
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