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an asteroid is going to hit the earth to calculate its distance it is observed from 2 diametrically opposite points a and b on earth the angle subtended at the asteroid by these two directions of observations is 2 ° given the diameter of earth to be about 1.276 × 10^7 m . compute the distance of the asteroid.
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Answers
Answer:
The moon is the earth’s satellite which revolves around it. The scientists have found the distance to this celestial object and others a long time ago using trigonometry without really being into space. The above details are from such an experiment where we find the distance from the moon to the earth using some known parameters.
We are informed that two teams observe the moon from the diametrically opposite points on the earth, say A and B at the same time as shown in the figure below.
The angle subtended at the moon due to the observation is 1054′
. Also, the diameter of the earth is given as 1.276×107m
.
Now, let us consider the above figure as two right angled triangles with the angle at the moon being the half of the original angle subtended. The arm AB and BC of the triangles constitute the radius of the earth, which is half the diameter.
We can use the trigonometric relations to find the distance BD which is the distance from the moon to the earth as –
In ΔABD,tanθ2=ABBD⇒BD=ABtanθ2but,AB=1.276×107m2=6.38×106mθ2=1054′2=12(1+5460)π180rad⇒θ2=0.0166rad
We can find the unknown parameter BD as –
BD=ABtanθ2⇒BD=6.38×106mtan(0.0166)⇒BD=6.38×106m0.0166∴BD=3.84337×108m
The distance from the moon to the earth is 384,337km. This is the required solution.
Note:
The distance we found from the moon to the earth is an average distance which can change during the different phases and position of earth and moon. The trigonometric relation was used by the earlier scientists which gave accurate measurements at each time of the year