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Chapter 5: Q45. (page 134)

A space shuttle releases a satellite into a circular orbit 780 km above the Earth. How fast must the shuttle be moving (relative to Earth’s center) when the release occurs?

Short Answer

Expert verified

The speed of the shuttle is 7.46×103m/s.

Step by step solution

01

Step 1. Given Data

The distance above the Earth is r=780km.

02

Step 2. Understanding the relation of speed of the space shuttle

In this problem, for calculating the speed of the space shuttle the relation of orbital speed will be used. Also, consider the value of radius as well as mass of the Earth.

03

Step 3. Estimating the speed of the space shuttle

The relation of orbital speedis given by,

v=GmErE+r

Here, G is the gravitational constant, rEis the radius of the Earth and mEis the mass of the Earth.

On plugging the values in the above relation.

v=6.67×10-11N·m2/kg25.98×1024kg6.38×106m+780km×1000m1kmv=7.46×103m/s

Thus, v=7.46×103m/sis the required speed.

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