Concept explainers
To plot: Acceleration a against probe position
To determine: The mass of the asteroid.

Answer to Problem 65P
The mass of the asteroid is
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:
Here, G is the constant of universal gravitation with the value of
Find the value of
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
Find the value of
Similarly convert the remaining acceleration values and also find the value of
Table 1 shows the acceleration (a) and
Acceleration
| Acceleration
| Position of the probe
| Value of
|
0.172 | 0.000172 | 80.0 |
|
0.353 | 0.000353 | 55.0 |
|
0.704 | 0.000704 | 40.0 |
|
0.858 | 0.000858 | 35.0 |
|
1.18 | 0.00118 | 30.0 |
|
Use Column (2) and Column (4) values to plot
Sketch of
Refer Figure 1.
The slope of the line is
Slope is equal to GM.
Substitute
Therefore, the mass of the asteroid is
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