Задача №45.25
Условие
В момент, когда приближающийся к Луне космический корабль находится на расстоянии H от ее поверхности и имеет скорость v0, направленную к центру Луны, включается тормозной двигатель. Учитывая, что сила тяготения обратно пропорциональна квадрату расстояния от корабля до центра Луны и принимая, что масса корабля изменяется по закону m=m0e-αt (m0 — масса ракеты в момент включения тормозного двигателя, α — постоянное число), найти α, при котором корабль совершит мягкую посадку (т.е. будет иметь скорость прилунения, равную нулю). Эффективная скорость истечения газов ve постоянна. Радиус Луны R, ускорение силы тяжести на Луне gЛ.Решение
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1.1
1.2
1.3
1.4
1.5
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
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2.13
2.14
2.15
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2.17
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2.20
2.21
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2.25
2.26
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2.30
2.31
2.32
2.33
2.34
2.35
2.36
2.37
2.38
2.39
2.40
2.41
2.42
2.43
2.44
2.45
2.46
2.47
2.48
2.49
2.50
2.51
2.52
2.53
2.54
2.55
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11
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3.13
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3.20
3.21
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3.25
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3.33
3.34
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3.38
4.1
4.2
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4.4
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4.6
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4.56
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5.1
5.2
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6.1
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8.1
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9.1
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9.3
9.4
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9.27
10.1
10.2
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11.1
11.2
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12.1
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13.1
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14.1
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15.1
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16.1
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17.1
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18.1
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18.41
19.1
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20.1
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20.13
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21.2
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22.1
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23.1
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23.48
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23.54
23.55
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23.60
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23.62
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23.64
23.65
23.66
23.67
23.68
23.69
23.70
23.71
24.1
24.2
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24.6
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24.31
24.34
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24.36
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24.46
25.1
25.2
25.3
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26.1
26.2
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26.4
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26.6
26.7
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26.20
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26.26
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26.31
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26.33
26.34
26.35
27.1
27.2
27.3
27.4
27.5
27.6
27.7
27.8
27.9
27.10
27.11
27.12
27.13
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27.20
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27.22
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27.24
27.25
27.26
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27.30
27.32
27.33
27.34
27.35
27.36
27.37
27.38
27.39
27.40
27.41
27.42
27.43
27.44
27.45
27.46
27.47
27.48
27.49
27.50
27.51
27.52
27.54
27.55
27.58
27.59
27.60
27.61
27.62
27.63
27.64
27.65
28.1
28.2
28.3
28.4
28.5
28.6
28.7
28.8
28.9
28.10
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29.1
29.2
29.3
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29.6
29.7
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29.9
29.10
29.11
29.12
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30.1
30.2
30.3
30.4
30.5
30.6
30.7
30.8
30.9
30.10
30.11
30.12
30.13
30.14
30.15
30.16
30.17
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30.19
30.20
30.21
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30.24
30.25
30.26
30.27
30.28
30.29
30.30
31.1
31.2
31.3
31.4
31.5
31.6
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31.11
31.13
31.14
31.15
31.16
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31.21
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31.25
31.26
31.27
31.28
31.29
31.30
31.31
31.32
31.33
31.34
31.35
32.1
32.2
32.3
32.4
32.5
32.6
32.7
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32.10
32.11
32.12
32.13
32.14
32.15
32.16
32.17
32.18
32.19
32.20
32.21
32.22
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32.24
32.25
32.26
32.27
32.28
32.29
32.30
32.31
32.32
32.33
32.34
32.35
32.36
32.37
32.38
32.39
32.40
32.41
32.42
32.43
32.44
32.45
32.46
32.47
32.48
32.49
32.50
32.51
32.52
32.53
32.54
32.55
32.56
32.57
32.58
32.59
32.60
32.61
32.62
32.63
32.64
32.65
32.66
32.67
32.68
32.69
32.70
32.71
32.72
32.73
32.74
32.75
32.76
32.77
32.79
32.80
32.81
32.82
32.83
32.84
32.85
32.86
32.87
32.88
32.89
32.90
32.91
32.92
32.93
32.94
32.95
32.96
32.97
32.98
32.99
32.100
32.101
32.102
32.103
32.104
32.105
32.106
32.107
33.1
33.2
33.3
33.4
33.5
33.6
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33.12
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33.14
33.15
33.16
33.17
33.18
33.19
33.20
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33.22
34.1
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34.5
34.6
34.7
34.8
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34.10
34.11
34.12
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34.30
34.31
35.1
35.2
35.3
35.4
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35.12
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35.14
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36.1
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36.14
37.1
37.2
37.3
37.4
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37.11
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37.33
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37.53
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37.55
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37.59
38.1
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38.5
38.6
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38.32
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38.38
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38.53
39.1
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40.1
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41.1
41.2
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42.1
42.2
42.3
42.4
42.5
42.6
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43.1
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43.13
44.1
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45.3
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46.1
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47.1
47.2
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48.1
48.5
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48.38
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48.44
48.48
48.49
49.1
49.2
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49.11
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53.5
53.12
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54.1
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54.32
54.33
54.35
55.2
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55.38
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55.44
56.3
56.7
56.9