Question

The Tethered Satellite discussed in this module is producing 5.00 kV, and a current of 10.0 A flows. (a) What magnetic drag force does this produce if the system is moving at 7.80 km/s? (b) How much kinetic energy is removed from the system in 1.00 h, neglecting any change in altitude or velocity during that time? (c) What is the change in velocity if the mass of the system is 100,000 kg? (d) Discuss the long term consequences (say, a week-long mission) on the space shuttle’s orbit, noting what effect a decrease in velocity has and assessing the magnitude of the effect.

Answer 1

Answer:

The answers as per the given problem is solved in the segment below.

Explanation:

According to the question,

(a)

$F=ILB$

By putting the values, we get

   $=10(2\times 10^4)(5\times 10^{-5})$

   $=10 \ N$

(b)

$W=Fx$

or,

    $=Fvt$

    $=10(7.80\times 10^3)(3600)$

    $=2.81\times 10^8 \ J$

(c)

$\frac{1}{2}mv'^2 =\frac{1}{2}mv^2-\omega$

or,

      $v=[v^2-\frac{2 \omega}{m} ]^\frac{1}{2}$

         $=[(7.8\times 10^3)^2-\frac{2(2.81\times 10^8)}{1\times 10^5} ]^{\frac{1}{2} }$

         $=7.79\times 10^3 \ m/s$

now,

$\Delta v=v-v'$

     $=0.36 \ m/s$

(d)

• The speed difference is around 1 percent throughout a week's trip. Generally, a decrease throughout the speed will indeed lead the orbit towards spiral inwards, ever since the speed would not have been adequate to maintain that rotational velocity.
• As nothing more than a result, this same shuttle could very well could use a little more propellant to sustain the velocity of aspiration if the orbit were ever to spiral somewhat within the vehicle.