Calculate the speed of a satellite moving in a circular orbit about the Earth at a height of 2700×10^3 m. The mass of the Earth is 5.98×10^24 kg and the mass of the satellite is 1400 kg.
Please show where you got stuck on this. I do not need practice.
By the way, if the satellite mass changes, what happens to the answer?
Force centripital=Force of gravity
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To calculate the speed of a satellite, we can use the formula for centripetal force:
Fc = (mv^2) / r
Where:
- Fc is the centripetal force
- m is the mass of the satellite
- v is the speed of the satellite
- r is the distance between the satellite and the center of the Earth
The centripetal force is provided by the gravitational force between the Earth and the satellite:
Fc = G * (m * M) / r^2
Where:
- G is the gravitational constant (6.67430 × 10^-11 N(m/kg)^2)
- M is the mass of the Earth
Setting these two equations equal to each other, we have:
G * (m * M) / r^2 = (m * v^2) / r
Now we can solve for the speed of the satellite (v).
First, rearrange the equation:
v^2 = (G * M) / r
Take the square root to solve for v:
v = √[(G * M) / r]
Now, substitute the values:
v = √[(6.67430 × 10^-11 N(m/kg)^2) * (5.98 × 10^24 kg) / (2700 × 10^3 m)]
Calculating this, we find:
v ≈ 7669 m/s
Therefore, the speed of the satellite in a circular orbit around the Earth at a height of 2700×10^3 m is approximately 7669 m/s.