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Dulcecandyy9396
21.04.2020 •
Mathematics
The first artificial satellite to orbit Earth was Sputnik I, launched by the Soviet Union in 1957. The orbit was an ellipse with Earth's center as one focus. The orbit's highest point above Earth's surface was 583 miles, and its lowest point was 132 miles.a) find an equation of the orbit.b) how far from Earth is the other focus?c) What is the length of the major axis?
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Ответ:
A) (x²/127806.25) + (y²/76956) = 1
B) 451 miles
C) 715 miles
Step-by-step explanation:
Center is at (0,0) and focus is at (c,0) while vertex is at (a,0)
Thus, a - c = 132 miles
and a + c=583 miles
Adding both equations together, we have;
2a= 715 miles
Thus, a = 715/2
a = 357.5 miles
Since a+c=583
Thus, c = 583-357.5 = 225.5 miles
Now, for an ellipse it is defined by; a² = b² + c²
a² = 357.5² = 127806.25
c² = 225.5² = 50850.25
So, b² = 127806.25 - 50850.25
b² = 76956
b = √76956
b = 277.409
A) Equation of tangent to ellipse which is equation of orbit would be;
(x²/a²) + (y²/b²) = 1
Thus,
(x²/127806.25) + (y²/76956) = 1
B) distance between the earth and the other focus is = 2c = 2 x 225.5 = 451 miles
C) Length of other major axis = 2a = 2 x 357.5 = 715 miles
Ответ:
21x=19x+4000
minus 19x
then divide by 2
×=2000