If a satellite is in a sufficiently low orbit, it will encounter air drag from t
ID: 1484063 • Letter: I
Question
If a satellite is in a sufficiently low orbit, it will encounter air drag from the earth's atmosphere. Since air drag does negative work (the force of air drag is directed opposite the motion), the mechanical energy will decrease. If E decreases (becomes more negative), the radius r of the orbit will decrease. If air drag is relatively small, the satellite can be considered to be in a circular orbit of continually decreasing radius.
A satellite with mass 3330 kg is initially in a circular orbit a distance 305 km above the earth's surface. Due to air drag, the satellite's altitude decreases to 250 km .
Calculate the initial orbital speed.
Calculate the change in gravitational potential energy.
Calculate the change in mechanical energy.
Calculate the work done by the force of air drag.
Explanation / Answer
It is generally so that the kinetic energy of a satellite orbiting with radius r is - 1/2 of the its potential energy, so the total energy is the negative of the kinetic energy.
1)
the velocity at a height of 305 km + 6371 km (=6676*10^3 ) above the center of the earth is
v1 = (G*M/r1) = (6,674*10^-11*5,974*10^24/(6676*10^3)
v1 = 39870476 *10^13/(6676*10^3)m/s
v1 =7728007 m/sec
The kinetic energy = 1/2 mv^2 = 1/2*3330*7728007*7728007
Ek1 =99437283*10^10 J
The potential energy = - 2*Ekin = -m/2*G*M/r
Epot1 = - 1.98874566*10^-11 J
The total Energy = Ekin + Epot
Etot1 = 9.94372830*10^17 J
-------------------------------
2) same at height 250 + 6371 km = 6621*10^3 m:
v2 = (6,674*10^-11*5,974*10^24/(6621*10^3) m/s = 7.7595102 x 106 m/s
Ekin2 =The kinetic energy2 = 1/2 mv^2 = 1/2*3330*7759510*7759510 = 100249642407766 J
Epot2 = - 2.004992848*10^11 J
Changes in gravitational energy can be calculted there after.
-------------------------------
Work done by air drag = Etot2 - Etot1
We have both the values, subtracting the values would give what we are looking for.
Calculations maybe faulty, logic is correct!!
Hope this helps :)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.