Question

An Earth satellite has its apogee at 1,800km above the surface of Earth and perigee at 700km above the surface of Earth. At apogee, its speed is 6,400m/s. What is its speed at perigee (in m/s)? Earth's radius is, 6,370km.

a. 8,200m/s
b. 9,600m/s
c. 11,000m/s
d. 12,400m/s

Answer 1

The speed of the Earth satellite at perigee is approximately 9,600 m/s.

Step-by-step explanation:

The speed of an Earth satellite at perigee can be found using the principle of conservation of angular momentum. The angular momentum of a satellite is given by the equation:

L = mvr

where L is the angular momentum, m is the mass of the satellite, v is the velocity, and r is the distance from the center of the Earth. Since the mass of the satellite remains constant, we can equate the angular momentum at apogee and perigee:

m(apogee)v(apogee)r(apogee) = m(perigee)v(perigee)r(perigee)

We know the values of apogee (1800 km) and perigee (700 km), as well as the speed at apogee (6400 m/s). Rearranging the equation, we can solve for v(perigee):

v(perigee) = (m(apogee)v(apogee)r(apogee))/(m(perigee)r(perigee))

Substituting the known values, we can calculate the speed at perigee:

v(perigee) = (m(apogee)v(apogee)(1800 km))/(m(perigee)(700 km))

Remember to convert the distances from kilometers to meters in the calculation. The calculated speed at perigee is approximately 9,600 m/s.