Satellite A is orbiting earth at an altitude of 500 km and satellite B is orbiting 800 km above the surface. How does the velocity of satellite a compare to the velocity of satellite b?
A) it depends on the masses of the satellites
B) the velocity of satellite B is equal to the velocity of satellite A
C) the velocity of satellite A is greater than the velocity of satellite b
D) the velocity of satellite a is less than the velocity of satellite b
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The answer is that the velocity of satellite A is greater than the velocity of satellite B
To determine the velocity of a satellite, we need to consider its distance from the center of the Earth and the Earth's mass. The velocity is influenced by the gravitational force between the satellite and the Earth.
The formula for the orbital velocity of a satellite is given by:
V = √(GM/R)
Where:
V = Velocity of the satellite
G = Gravitational constant, approximately 6.67 × 10^-11 N(m/kg)^2
M = Mass of the Earth
R = Distance between the center of the Earth and the satellite
Satellite A is orbiting at an altitude of 500 km above the Earth's surface, which means its distance from the center of the Earth is equal to the Earth's radius plus 500 km.
Satellite B is orbiting at an altitude of 800 km above the Earth's surface, which means its distance from the center of the Earth is equal to the Earth's radius plus 800 km.
Since the altitude of satellite B is greater than that of satellite A, the distance R for satellite B is larger than for satellite A.
If we compare their velocities using the formula, we can see that both satellites have the same mass (as it is not mentioned in the question), which means the mass does not affect the velocity.
As the distance R increases, the velocity decreases, so the satellite with the smaller distance (satellite A) will have a greater velocity than the satellite with the larger distance (satellite B).
Therefore, the correct answer is:
C) the velocity of satellite A is greater than the velocity of satellite B.