Determine the Altitude of a Satellite above Earth Given it's Constant Speed

[PhysicsJunkie]

Homework Statement

A remote-sensing satellite travels in a circular orbit at a constant speed of 8.2 x 10^3 m/s. Determing the altitude in kilometres of the satellite above Earth's surface.

Homework Equations

Fc = FG

The Attempt at a Solution

mv^2/r = GMm/r^2
v^2 = GM/r
r = GM/v^2
r = (6.67 x 10^-11 * 5.98 x 10^24)/(8.2 x 10^3)^2
r = 5931975 m - radius of Earth (6.38 x 10^6 m)
r = NEGATIVE NUMBER

Why am I getting a negative number? Is there a mistake in my conversions or am I completely off as to how to solve this? Any help will be greatly appreciated. :)

 

[LowlyPion]

Using μ = G*M ≈ 400,000 (if you keep things in km), I get V²= 400,000/(8.2)² = 5948 km.

Maybe it's a fast Earth worm?

 

[nlightner]

There are a few possible reasons why you are getting a negative number for the altitude of the satellite. Here are some things to consider:

1. Check your units: When solving equations, it's important to make sure that all of your units are consistent. In this case, the units for mass and radius should be in kilograms and meters, respectively. Make sure that you are using the correct values for these quantities in your calculations.

2. Consider the direction of the forces: In the equation Fc = FG, Fc represents the centripetal force and FG represents the force of gravity. These forces are acting in opposite directions, so they should have opposite signs in your equation. Make sure that you are accounting for this in your calculations.

3. Check your order of operations: When using a calculator, it's important to make sure that you are entering the calculations in the correct order. For example, if you enter (6.67 x 10^-11 * 5.98 x 10^24)/(8.2 x 10^3)^2, the calculator will first square the denominator and then divide, which will give you a different result than if you first divide and then square. Make sure that you are using parentheses to indicate the correct order of operations.

4. Consider the difference between radius and altitude: The equation you are using, r = (GM)/v^2, gives you the radius of the circular orbit. This is the distance from the center of the Earth to the satellite. To find the altitude, you need to subtract the radius of the Earth from this value. So, in your final answer, you should have r - 6.38 x 10^6 m.

I hope this helps and good luck with your homework! Remember to always double-check your calculations and units to avoid mistakes.