(a) What linear speed must an Earth satellite have to be in a circular orbit at an altitude of 153 km?

m/s

(b) What is the period of revolution?
min
Read the eBook

= te gravitational constantThe speed required to hold a satellite in a circular orbit derives from V = sqrt(µ/r) where V = the orbital speed in feet/sec., r = the orbital radius in feet and µ = the gravitational constant of the earth = 1.407974x10^16, ft.^3/sec.^2 or 3.986365x10^14 m^2/sec.^2.

Using the earth radius of 3963 miles, or 6378 km, r becomes 6378 + 153 = 6531 km. or 6531000m. Then V = sqrt(3.986365x10^14/6531000) = 7812.65m/s or.

The orbital period derives from T = 2(Pi)sqrt(r^3/µ).

thank you!!!

To find the linear speed of an Earth satellite in a circular orbit at a given altitude, we can use the following formula:

v = √(GM/r)

where:
v is the linear speed,
G is the gravitational constant (approximately 6.67 × 10^-11 N(m/kg)^2),
M is the mass of the Earth (approximately 5.97 × 10^24 kg), and
r is the distance from the center of the Earth to the center of the satellite.

For part (a), we are given the altitude of the satellite, which we can convert to the distance from the center of the Earth by adding the Earth's radius, which is approximately 6,371 km or 6,371,000 meters.

So, r = 153 km + 6,371 km = 6,524,000 meters.

Now, we can plug the values into the formula to find the linear speed:

v = √(6.67 × 10^-11 N(m/kg)^2 × 5.97 × 10^24 kg / 6,524,000 meters)

After calculating this, we get the linear speed in m/s.

For part (b), to find the period of revolution, we can use the following formula:

T = 2πr / v

where:
T is the period of revolution,
r is the distance from the center of the Earth to the center of the satellite, and
v is the linear speed.

We already know the value of r from part (a), and we can use the same value for v. We can plug these values into the formula to find the period of revolution in seconds.

To convert the period of revolution to minutes, we divide it by 60.

Thus, we can determine the values for both parts (a) and (b) by using these formulas and the given information.