z
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
4000000
4500000
5000000
5500000
6000000
6500000
7000000
7500000
8000000
8500000
9000000
9500000
10000000
10500000
11000000
11500000
12000000
12500000
13000000
13500000
14000000
14500000
15000000
15500000
16000000
16500000
17000000
17500000
18000000
18500000
19000000
19500000
20000000
20500000
21000000
21500000
22000000
22500000
G
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
M
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
Re
g
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
g0
9.800416
8.427314
7.323796
6.423646
5.679797
5.058052
4.533077
4.085785
3.701572
3.369112
3.079510
2.825706
2.602032
2.403902
2.227569
2.069950
1.928486
1.801044
1.685830
1.581328
1.486250
1.399496
1.320122
1.247314
1.180367
1.118669
1.061685
1.008947
0.960042
0.914610
0.872327
0.832910
0.796106
0.761689
0.729456
0.699226
0.670838
0.644143
0.619012
0.595322
0.572967
0.551848
0.531876
0.512968
0.495051
0.478057
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
g/g0
0.999329
0.859316
0.746793
0.655006
0.579157
0.515759
0.462229
0.416619
0.377442
0.343542
0.314011
0.288131
0.265324
0.245121
0.227141
0.211069
0.196644
0.183649
0.171901
0.161245
0.15155
0.142704
0.13461
0.127186
0.12036
0.114068
0.108258
0.10288
0.097894
0.093261
0.088949
0.08493
0.081177
0.077668
0.074381
0.071299
0.068404
0.065682
0.063119
0.060704
0.058424
0.056271
0.054234
0.052306
0.050479
0.048746
23000000
23500000
24000000
24500000
25000000
25500000
26000000
26500000
27000000
27500000
28000000
28500000
29000000
29500000
30000000
30500000
31000000
31500000
32000000
32500000
33000000
33500000
34000000
34500000
35000000
35500000
36000000
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
6.67E-11
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
5.97E+24
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
6.38E+06
0.461922
0.446592
0.432011
0.418134
0.404914
0.392312
0.380289
0.368810
0.357843
0.347359
0.337328
0.327726
0.318528
0.309711
0.301256
0.293143
0.285352
0.277869
0.270675
0.263758
0.257102
0.250696
0.244525
0.238580
0.232849
0.227322
0.221990
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
9.807
0.047101
0.045538
0.044051
0.042636
0.041288
0.040003
0.038777
0.037607
0.036489
0.035419
0.034397
0.033418
0.03248
0.031581
0.030718
0.029891
0.029097
0.028334
0.0276
0.026895
0.026216
0.025563
0.024934
0.024328
0.023743
0.02318
0.022636
Fernando Ayala Perez 343533
En el presente problema vamos a calcular la gravedad de la tierra en función de la altura hasta la
altura de una orbta geoestacionario (36000 km) con intervalos de 500 km, usando esta formula
Siendo G la constante de gravitación universal, M la masa de la tierea RE, el radio de la tierrza, y z
nuestra altura en intervalos de 500 Km, ya que la constante gravitaciónal usa metros en sus unidades
se convertiran la alturaz y Re de km a m.
G
6.67E-11 m3/(kg*s^2)
M
5.97E+24 kg
Re
6378 km= 6378000m
intervalo z 500 km=500,000 m
Graficamos la relación que hay entre la acelaracion gravitacional g0 que esta en z=0 a
z=36,000 km , y graficamos esta relación, como se puede ver esta grafica, conforme se va
aumentando la altura la acelerción disminuye en una relación inversamente proporcinal al
cuadrado de la distancia, como indica la ley de gravitación universal.
1.2
g/g0
1
0.8
0.6
0.4
0.2
0
1000000
2000000
3000000
4000000
5000000
6000000
7000000
8000000
9000000
10000000
11000000
12000000
13000000
14000000
15000000
16000000
17000000
18000000
19000000
20000000
21000000
22000000
23000000
24000000
25000000
26000000
27000000
28000000
29000000
30000000
31000000
32000000
33000000
34000000
35000000
36000000
0