Two satellites, x and y, are orbiting earth. satellite x is 1.2 × 106 m from earth, and satellite y is 1.9 × 105 m from earth. which best compares the satellites? satellite x has a greater period and a faster tangential speed than satellite y. satellite x has a greater period and a slower tangential speed than satellite y. satellite x has a shorter period and a faster tangential speed than satellite y. satellite x has a shorter period and a slower tangential speed than satellite y.

Satellite X has a greater period and a slower tangential speed than Satellite Y

Explanation:

According to Kepler’s Third Law of Planetary motion “The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”.

   (1)

Where;

is the Gravitational Constant

is the mass of the Earth

 is the semimajor axis of the orbit each satellite describes around Earth (assuming it is a circular orbit, the semimajor axis is equal to the radius of the orbit)

So for satellite X, the orbital period is:

   (2)

Where

   (3)

   (4)

For satellite Y, the orbital period is:

   (5)

Where

   (6)

   (7)

This means

Now let's calculate the tangential speed for both satellites:

For Satellite X:

(8)

(9)

For Satellite Y:

(10)

(11)

This means

Therefore:

Satellite X has a greater period and a slower tangential speed than Satellite Y

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