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Question 40293: 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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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?
Draw the picture putting center at (0,0), focus at (c,0) vertex at (a,0)
Then a-c=132 miles
and a+c=583 miles
So, 2a= 715 miles
a= 357.5 miles
a^2=127806.25
Since a+c=583
c= 583-357.5=225.5
c^2=50850.25
For an ellipse a^2=b^2+c^2
So, b^2= 127806.25-5050.25
b^2= 76956
b= 277.409
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a) find an equation of the orbit.
[x^2/127806.25]+[y^2/76956]=1
b) how far from Earth is the other focus?
2c=2(225.5)=451 mils
c) What is the length of the major axis?
2a=2*357.5)=715 miles
Cheers,
Stan H.
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