Consider problem U concerning the geosynchronous satellite of mass 50 kg. It orbits at a radius of 42,300 km with a speed of 3076 m/s. a) How much energy is needed to lift the satellite from the earth's surface (Re=6,370 km) up to that radius? b) How much kinetic energy does the satellite have as it orbits?Consider problem U concerning the geosynchronous satellite of mass 50 kg. It orbits at a radius of 42,300 km with a speed of 3076 m/s. a) How much energy is needed to lift the satellite from the earth's surface (Re=6,370 km) up to that radius? b) How much kinetic energy does the satellite have as it orbits?

Question

Consider problem U concerning the geosynchronous satellite of mass 50 kg. It orbits at a radius of 42,300 km with a speed of 3076 m/s. a) How much energy is needed to lift the satellite from the earth's surface (Re=6,370 km) up to that radius? b) How much kinetic energy does the satellite have as it orbits?Consider problem U concerning the geosynchronous satellite of mass 50 kg. It orbits at a radius of 42,300 km with a speed of 3076 m/s. a) How much energy is needed to lift the satellite from the earth's surface (Re=6,370 km) up to that radius? b) How much kinetic energy does the satellite have as it orbits?

Answer 1

To solve this problem, we need to use the concepts of potential energy and kinetic energy.

a) To calculate the energy needed to lift the satellite from the Earth's surface to the given radius, we need to find the change in potential energy between the two positions. The potential energy can be calculated using the formula:

Potential Energy = mass * gravitational acceleration * height

The gravitational acceleration on Earth's surface is approximately 9.8 m/s^2. The height is the difference in radius between the satellite's orbit and the Earth's surface.

Let's calculate the height first:

Height = Final radius - Initial radius
= 42,300 km - 6,370 km
= 35,930 km

To convert this height into meters, multiply by 1000:

Height = 35,930 km * 1000 m/km
= 35,930,000 m

Now, we can calculate the potential energy:

Potential Energy = mass * gravitational acceleration * height
= 50 kg * 9.8 m/s^2 * 35,930,000 m
= 17,627,000,000 J

Therefore, the energy needed to lift the satellite to the given radius is approximately 17,627,000,000 Joules.

b) The kinetic energy of the satellite as it orbits can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Given that the mass of the satellite is 50 kg and the velocity is 3076 m/s, we can plug in these values into the formula:

Kinetic Energy = (1/2) * 50 kg * (3076 m/s)^2
= 23,660,600 J

Therefore, the kinetic energy of the satellite as it orbits is approximately 23,660,600 Joules.