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Chapter 13: Q. 10 (page 353)

Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times. As a satellite spirals inward, does it speed up, slow down, or maintain the same speed? Explain.

Short Answer

Expert verified

Speed will increase as it spiral inwards.

Step by step solution

01

Given Information

Satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere.

02

Explanation

From Keplar's law period of an orbit is given by

T2 = R3

So T = R3/2

We see as the radius decreases the time period of the orbit will also decrease. And angular velocity will increase.

As angular velocity is given by 蠅 = 2蟺/T.

which is inversely proportional to the period T.

So we can conclude that as the satellite spirals inward, speed will increase.

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Most popular questions from this chapter

You are the science officer on a visit to a distant solar system. Prior to landing on a planet you measure its diameter to be 1.8脳107mand its rotation period to be role="math" localid="1648535932335" 22.3hours.You have previously determined that the planet orbits 2.2脳脳1011mfrom its star with a period of 402earthdays. Once on the surface you find that the free-fall acceleration is 12.2m/s2.What is the mass of (a) the planet and (b) the star?

A space station orbits the sun at the same distance as the earth but on the opposite side of the sun. A small probe is fired away from the station. What minimum speed does the probe need to escape the solar system?

Two spherical objects have a combined mass of 150kg.The gravitational attraction between them is 8.00脳10-6Nwhen their centers are 20cmapart. What is the mass of each?

Let鈥檚 look in more detail at how a satellite is moved from one circular orbit to another. FIGURE CP13.71shows two circular orbits, of radii localid="1651418485730" r1and localid="1651418489556" r2, and an elliptical orbit that connects them. Points 1and 2are at the ends of the semimajor axis of the ellipse.

a. A satellite moving along the elliptical orbit has to satisfy two conservation laws. Use these two laws to prove that the velocities at points localid="1651418503699" 1and localid="1651418499267" 2are localid="1651418492993" v1鈥�=2GMr2/r1r1+r2and localid="1651418509687" v2鈥�=2GMr1/r2r1+r2The prime indicates that these are the velocities on the elliptical orbit. Both reduce to Equation 13.22if localid="1651418513535" r1=r2=r.

b. Consider a localid="1651418519576" 1000kgcommunications satellite that needs to be boosted from an orbit localid="1651418573632" 300kmabove the earth to a geosynchronous orbit localid="1651418578672" 35,900kmabove the earth. Find the velocity localid="1651418584351" v1on the inner circular orbit and the velocity localid="1651418590277" v=1at the low point on the elliptical orbit that spans the two circular orbits.

c. How much work must the rocket motor do to transfer the satellite from the circular orbit to the elliptical orbit?

d. Now find the velocity localid="1651418596735" v=2at the high point of the elliptical orbit and the velocity v2 of the outer circular orbit.

e. How much work must the rocket motor do to transfer the satellite from the elliptical orbit to the outer circular orbit?

f. Compute the total work done and compare your answer to the result of Example localid="1651418602767" 13.6.

What is the total gravitational potential energy of the three masses in FIGUREP13.35?
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