HELP PLEASE!!! A satellite moves in a circular orbit around Earth at a speed of 5085 m/s.

(a) Determine the satellite's altitude above the surface of Earth.
(b) Determine the period of the satellite's orbit.

centripetal force: mv^2/r

where r is distance from CENTER of Earth.
then set this equal to gravitational force

GMem/r^2

GMe/r^2=v^2/r solve for r, then subtract Radiusearth to get altitude.

To find the answers to these questions, we can use some principles of circular motion and the laws of gravitation.

(a) To determine the satellite's altitude above the surface of the Earth, we need to use the centripetal force equation in circular motion, which is given by:

Fc = mv^2 / r

Where Fc is the centripetal force, m is the mass of the satellite, v is the speed of the satellite, and r is the radius of the circular orbit.

In this case, the centripetal force is provided by the gravitational force between the Earth and the satellite, which can be expressed using the law of gravitation:

Fc = G * (m * Me) / r^2

Where G is the gravitational constant and Me is the mass of the Earth.

Equating these two equations, we have:

mv^2 / r = G * (m * Me) / r^2

Canceling out the mass of the satellite, we get:

v^2 / r = G * Me / r^2

Simplifying further:

r = (G * Me * r^2) / v^2

Now we can plug in the known values to find the altitude above the surface of the Earth:

G = 6.6743 × 10^-11 m^3 / (kg * s^2) (gravitational constant)
Me = 5.972 × 10^24 kg (mass of the Earth)
v = 5085 m/s (speed of the satellite)

r = ((6.6743 × 10^-11 m^3 / (kg * s^2)) * (5.972 × 10^24 kg) * r^2) / (5085 m/s)^2

Solving this equation will give us the radius, and then we can subtract the Earth's radius (6371000 m) to find the satellite's altitude above the surface of the Earth.

(b) To determine the period of the satellite's orbit, we use the formula:

T = (2πr) / v

Where T is the period, r is the radius of the orbit, and v is the velocity of the satellite.

Again, we can substitute the radius we found in part (a) and the given velocity to calculate the period.