Math Is Fun Forum

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Find Equation for Orbit of Satellite

Earth is represented on a map of a portion of the solar system so that it's surface is the center with equation
x^2 + y^2 + 2x + 4y - 4091 = 0. A weather satellite circles 0.6 units above Earth with the center of its circular orbit at the center of Earth. Find an equation for the orbit of the satellite.

Let's see what happens here.

I think the question is asking to convert the given equation in general form to the standard form of an equation of a circle. If that's the case, why not say that specifically? Ridiculous!!!

x^2 + y^2 + 2x + 4y - 4091 = 0

I think rearranging some of the terms helps out.

x^2 + 2x + y^2 + 4y - 4091 = 0

Completing the square is needed on the terms x^2 + 2x and y^2 + 4y.

After completing the square, I got

x^2 + 2x + 1 and y^2 + 4y + 4.

This leads (x + 1)(x + 1) + (y + 2)(y + 2) - 4091 = 0.

On the right side, add 1 + 4 + 4091 to get 4096.

I think the equation is (x + 1)^2 + (y + 2)^2 = 4096.

You say?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,198

Re: Find Equation for Orbit of Satellite

I agree the question is strangely worded.

I think the circumference is the surface of the Earth and the centre is at (-1 . -2).

The radius is root(4096)

The satellite of 0.6 above the surface so it's radius is root(4096) + 0.6

Just before your final equation there's 1 + 4 missing on the RHS  but you have it correctly on the next line  so no worries.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

nycguitarguy

Member

Registered: 2024-02-24

Posts: 549

Re: Find Equation for Orbit of Satellite

I agree the question is strangely worded.

I think the circumference is the surface of the Earth and the centre is at (-1 . -2).

The radius is root(4096)

The satellite of 0.6 above the surface so it's radius is root(4096) + 0.6

Just before your final equation there's 1 + 4 missing on the RHS  but you have it correctly on the next line  so no worries.

Bob

I got the right answer doing the wrong work.