Question
Carpets of satellites quick check let g be the universal gravitational constant and m be the mass of the planet and satellite it's organic which equation would be used to find the velocity of the satellite if it is placed in a low earth orbit
Answers
Answered by
GPT-4o mini
To find the velocity of a satellite in low Earth orbit (LEO), you can use the formula derived from the concept of gravitational force and centripetal force. The equation is given by:
\[
v = \sqrt{\frac{G \cdot M}{r}}
\]
Where:
- \( v \) is the orbital velocity of the satellite,
- \( G \) is the universal gravitational constant (approximately \( 6.674 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \)),
- \( M \) is the mass of the Earth (approximately \( 5.972 \times 10^{24} \, \text{kg} \)),
- \( r \) is the total distance from the center of the Earth to the satellite (which is equal to the radius of the Earth plus the altitude of the satellite).
In low Earth orbit, typical altitudes are around 200 km to 2,000 km above the Earth's surface, so \( r \) would be the Earth's average radius (approximately \( 6,371 \, \text{km} \)) plus the satellite's altitude from the Earth's surface.
So, you would plug in the values for \( G \), \( M \), and \( r \) to determine the velocity \( v \) of the satellite in low Earth orbit.
\[
v = \sqrt{\frac{G \cdot M}{r}}
\]
Where:
- \( v \) is the orbital velocity of the satellite,
- \( G \) is the universal gravitational constant (approximately \( 6.674 \times 10^{-11} \, \text{m}^3 \, \text{kg}^{-1} \, \text{s}^{-2} \)),
- \( M \) is the mass of the Earth (approximately \( 5.972 \times 10^{24} \, \text{kg} \)),
- \( r \) is the total distance from the center of the Earth to the satellite (which is equal to the radius of the Earth plus the altitude of the satellite).
In low Earth orbit, typical altitudes are around 200 km to 2,000 km above the Earth's surface, so \( r \) would be the Earth's average radius (approximately \( 6,371 \, \text{km} \)) plus the satellite's altitude from the Earth's surface.
So, you would plug in the values for \( G \), \( M \), and \( r \) to determine the velocity \( v \) of the satellite in low Earth orbit.
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