A satellite is orbit about earth, its orbital radius is 3.43*10e7m.The mass of the satellite is 9166kg and the mass of earth is 5.974*10e24kg. Determine the orbital speed of the satellite in mi/s. 1mi/s=1609m/s.
To determine the orbital speed of the satellite, we can make use of the concept of centripetal force.
The centripetal force acting on the satellite is provided by the gravitational force between the satellite and the Earth. It can be expressed using the formula:
F = (G * m₁ * m₂) / r²
Where,
F is the force of gravity,
G is the gravitational constant (6.67430 x 10^-11 N m²/kg²),
m₁ is the mass of the satellite,
m₂ is the mass of the Earth,
and r is the orbital radius.
Now, we can calculate the force of gravity acting on the satellite:
F = (G * m₁ * m₂) / r²
F = (6.67430 x 10^-11 N m²/kg²) * (9166 kg) * (5.974 x 10^24 kg) / (3.43 x 10^7 m)²
Next, we can equate the centripetal force to the gravitational force:
F = m * v² / r
Where,
v is the orbital speed of the satellite.
We rearrange the equation to solve for v:
v = √(F * r / m)
Now, let's calculate the orbital speed:
v = √((6.67430 x 10^-11 N m²/kg²) * (9166 kg) * (5.974 x 10^24 kg) / (3.43 x 10^7 m)²)
Once we find the orbital speed in m/s, we can convert it to mi/s by multiplying it by the conversion factor:
1 mi/s = 1609 m/s
Therefore, to determine the orbital speed of the satellite in mi/s, we need to perform these calculations.