Find an equation of the circular orbit of a satellite 500 miles above the surface of earth. Place the origin of the rectangular coordinate system at the center of Earth and assume that the radius of Eatch is 4000 miles.
As I read your question,
wouldn't the centre be (0,0) and the radius 4500 ?
To find the equation of the circular orbit of a satellite 500 miles above the surface of the Earth, we can start by considering the formula for a circle in a rectangular coordinate system.
The equation of a circle with its center at the origin (0,0) and a radius of r can be written as:
x^2 + y^2 = r^2
In this case, the radius of the Earth is given as 4000 miles. Since the satellite is 500 miles above the surface of the Earth, the effective radius of the orbit would be 4000 + 500 = 4500 miles.
Therefore, the equation of the circular orbit with the origin at the center of the Earth would be:
x^2 + y^2 = 4500^2
Simplifying the equation, we get:
x^2 + y^2 = 20,250,000
So, the equation of the circular orbit of the satellite is x^2 + y^2 = 20,250,000.
To find an equation for the circular orbit of a satellite 500 miles above the surface of Earth, we can use the equation for a circle centered at the origin of a coordinate system.
Given that the radius of Earth is 4000 miles, we can determine the radius of the satellite's orbit by adding the altitude of the satellite (500 miles) to the radius of Earth.
The total radius would be 4000 miles + 500 miles = 4500 miles.
Now, using the equation for a circle, which is (x - h)^2 + (y - k)^2 = r^2, we can substitute the values:
(x - 0)^2 + (y - 0)^2 = 4500^2
Simplifying:
x^2 + y^2 = 20250000
So, the equation of the circular orbit of the satellite is x^2 + y^2 = 20250000.