Example  6  The Hubble Space Telescope
The mass of the Hubble Space Telescope is 11 600 kg. Determine the weight of the telescope (a) when it was resting on the earth and (b) as it is in its orbit 598 km above the earth's surface.
Figure 4.12    The weight of the Hubble Space Telescope decreases as the telescope gets farther from the earth. The distance from the center of the earth to the telescope is r.
Reasoning   The weight of the Hubble Space Telescope is the gravitational force exerted on it by the earth. According to Equation 4.4, the weight varies inversely as the square of the radial distance r. Thus, we expect the telescope's weight on the earth's surface (r smaller) to be greater than its weight in orbit (r larger).

Solution  
Problem-solving insight
When applying Newton's gravitation law to uniform spheres of matter, remember that the distance r is between the centers of the spheres, not between the surfaces.

(a)  
On the earth's surface, the weight is given by Equation 4.4 with r = 6.38 × 106 m (the earth's radius):
(b)  
When the telescope is 598 km above the surface, its distance from the center of the earth is
The weight now can be calculated as in part (a), except that the new value of r must be used: . As expected, the weight is less in orbit.



Copyright © 2010 John Wiley & Sons, Inc. All rights reserved.