The space shuttle, with mass 86,400 kg, is in a circular orbit of radius 6.66 ×10^6 m around the

step 1 In the given problem, mass of the space shuttle is given as it is 6 ,400 kilogram. Radius of the

The space shuttle, with mass 86,400 kg, is in a circular...

The space shuttle, with mass $86,400 \mathrm{kg},$ is in a circular orbit of radius $6.66 \times 10^{6} \mathrm{m}$ around the earth. It takes 90.1 min for the shuttle to complete each orbit. On a repair mission, the shuttle is cautiously moving 1.00 $\mathrm{m}$ closer to a disabled satellite every 3.00 s. Calculate the shuttle's kinetic energy (a) relative to the earth and (b) relative to the satellite.

Key Concepts

Circular Orbit

A circular orbit is a special case of orbital motion where an object moves around a central body with a constant distance (radius). In this situation, the gravitational force acts as the centripetal force necessary to maintain the circular motion. Understanding circular orbits helps in computing orbital speeds using the relationship between the radius, orbital period, and the velocity needed to sustain the orbit.

Kinetic Energy

Kinetic energy is the energy that an object possesses due to its motion, typically calculated using the formula KE = 1/2 m v², where m is the mass and v is the speed of the object. In orbital mechanics, the object has kinetic energy relative to a specific reference frame, and the calculation will depend on its velocity in that frame.

Orbital Velocity

Orbital velocity is the speed an object must have to stay in a stable orbit around a central body. For circular orbits, it can be determined by either balancing the gravitational force with the required centripetal force or by using the formula v = 2?r/T, where r is the orbital radius and T is the orbital period. This concept is essential for calculating kinetic energy in orbit.

Reference Frames and Relative Motion

The kinetic energy of an object is dependent on the reference frame from which it is observed. When comparing the kinetic energy relative to the Earth and relative to another object, such as a satellite, the velocity used in the calculation differs. This concept of relative motion explains that two observers moving with different velocities will measure different kinetic energies for the same object, highlighting the importance of specifying the frame of reference.

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