Satellite A is orbiting Earth at an altitude of 500 km and Satellite B is orbiting 800 km above the surface.

Question

How does the velocity of Satellite A compare to the velocity of Satellite B?

The velocity of Satellite A is greater than the velocity of Satellite B.

The velocity of Satellite A is less than the velocity of Satellite B.

The velocity of Satellite B is equal to the velocity of Satellite A.

It depends on the masses of the satellites.

Answer 1

The velocity of a satellite in orbit around Earth can be determined by the formula for orbital velocity, which is given by:

\[ v = \sqrt{\frac{GM}{r}} \]

where:

• \( v \) is the orbital velocity,
• \( G \) is the gravitational constant,
• \( M \) is the mass of the Earth, and
• \( r \) is the distance from the center of the Earth to the satellite.

The altitude of a satellite is measured from the Earth's surface, so to find the radius \( r \), you need to add the Earth's radius (approximately 6371 km) to the altitude.

For Satellite A:

• Altitude = 500 km
• Radius \( r_A = 6371 , \text{km} + 500 , \text{km} = 6871 , \text{km} \)

For Satellite B:

• Altitude = 800 km
• Radius \( r_B = 6371 , \text{km} + 800 , \text{km} = 7171 , \text{km} \)

Now, we can see how the velocities compare:

• Since \( r_B > r_A \), then \( \sqrt{r_B} > \sqrt{r_A} \).
• Consequently, since the orbital velocity is inversely proportional to the square root of the radius, it follows that \( v_A > v_B \).

Thus, the velocity of Satellite A is greater than the velocity of Satellite B.

The correct conclusion is:

The velocity of Satellite A is greater than the velocity of Satellite B.