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Chapter 8, Problem 65P
To determine

To plot: Acceleration a against probe position 1r2 .

To determine: The mass of the asteroid.

Expert Solution & Answer
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Answer to Problem 65P

The mass of the asteroid is 1.58×1016kg_ .

Explanation of Solution

Given information:

The acceleration and position of probe data are given.

Calculation:

The gravitational acceleration at the surface of the asteroid is shown below:

a=GMr2

Here, G is the constant of universal gravitation with the value of 6.67×1011Nm2/kg2 , MS is the mass of the asteroid, and r is the position of probe.

Find the value of 1r2 and plot a vs 1r2 to obtain the best fit line.

The slope of the graph provides the value of GM.

Divide the slope value by G to obtain the mass of the asteroid.

Convert the acceleration value of 0.172mm/s2 to m/s2 :

a = 0.172mm/s2= 0.172mm/s2(103m1mm)=0.000172m/s2

Find the value of 1r2 for the r value of 80.0 km.

1r2=1(80.0km)2=1(80.0km×103m1km)2=1.5625×1010

Similarly convert the remaining acceleration values and also find the value of 1r2 for the remaining data.

Table 1 shows the acceleration (a) and 1r2 values .

Acceleration a(mm/s2) Acceleration a(m/s2) Position of the probe r(km) Value of 1r2
0.1720.00017280.0 1.5625×1010
0.3530.00035355.0 3.3058×1010
0.7040.00070440.0 6.25×1010
0.8580.00085835.0 8.1633×1010
1.180.0011830.0 1.1111×109

Use Column (2) and Column (4) values to plot a(m/s2) versus 1r2 .

Sketch of a(m/s2) versus 1r2 is shown in Figure 1.

Essential University Physics: Volume 1; Mastering Physics with Pearson eText -- ValuePack Access Card -- for Essential University Physics (3rd Edition), Chapter 8, Problem 65P

Refer Figure 1.

The slope of the line is =1.054×106 .

Slope is equal to GM.

GM=1.054×106 (1)

Substitute 6.67×1011Nm2/kg2 for G to obtain the mass of the asteroid.

(6.67×1011)M=1.054×106M=1.054×1066.67×1011=1.58×1016kg

Therefore, the mass of the asteroid is 1.58×1016kg_ .

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Chapter 8 Solutions

Essential University Physics: Volume 1; Mastering Physics with Pearson eText -- ValuePack Access Card -- for Essential University Physics (3rd Edition)

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