A satellite is in a circular orbit around an unknown planet. The satellite has a speed of 1.65 104 m/s, and the radius of the orbit is 5.30 106 m. A second satellite also has a circular orbit around this same planet. The orbit of this second satellite has a radius of 8.60 106 m. What is the orbital speed of the second satellite?
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To find the orbital speed of the second satellite, we can use the concept of conservation of angular momentum.
The angular momentum of an object in circular motion is given by the equation:
L = mvr
where L is the angular momentum, m is the mass of the object, v is the velocity of the object, and r is the radius of the orbit.
Since both satellites are orbiting the same planet, their masses can be considered the same. Therefore, the angular momentum of the first satellite (L1) is equal to the angular momentum of the second satellite (L2):
L1 = L2
We can rearrange the equation to solve for the orbital speed of the second satellite (v2):
m1v1r1 = m2v2r2
Since the masses are the same, we can cancel them out:
v1r1 = v2r2
Now we can substitute the given values for the first satellite (v1 = 1.65 * 10^4 m/s and r1 = 5.30 * 10^6 m) and solve for the orbital speed of the second satellite (v2):
(1.65 * 10^4 m/s)(5.30 * 10^6 m) = v2(8.60 * 10^6 m)
Dividing both sides of the equation by (8.60 * 10^6 m), we get:
v2 = (1.65 * 10^4 m/s)(5.30 * 10^6 m) / (8.60 * 10^6 m)
v2 = 1.02 * 10^4 m/s
Therefore, the orbital speed of the second satellite is approximately 1.02 * 10^4 m/s.