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## Homework Statement

A rocket with a mass of 2kg and traveling at 14,008.34 meters/second loses 10% of its velocity as finishes the remainder of its trip out of earth's gravity field. Calculate the predicted orbital radius for the satellite based on the final velocity of the satellite, given that the mass of the earth is 5.97x1024 kg.

## Homework Equations

I feel like the angular kinematics equations would be important here, as would F=ma and some other formulas related to angular kinematics (see below)

**Angular kinematics formulas:**

ω

_{f}=ω

_{i}+αt

Δθ=ω

_{i}t+½αt

^{2}

ω

_{f}

^{2}=ω

_{i}

^{2}+2αΔθ

where ω is angular velocity, α is change in angular velocity, and

*t*is time.

**Other formulas:**

F=ma

V

_{t}=rω

where V

_{t}is tangential speed,

*r*is radius and ω is angular velocity.

There might be more formulas that should be here, but I can't think of any off the top of my head.

## The Attempt at a Solution

So, my eventual goal is to find the value of

*r.*Since I've been given the mass of Earth, I feel like I need to be doing something involving the gravitational force between the objects. We haven't gone over universal gravitation in our class yet, so I wouldn't imagine its anything to do with that. I'm assuming that the 12,607.506 meters/second I have for a new velocity after accounting for the 10% loss would become the tangential speed of the satellite.

I tried using good old F=ma to calculate the centripetal force, and got a value of 19.6 newtons, given the rocket's mass of 2kg and an acceleration due to gravity of 9.8 meters/second

^{2}. Where I'm getting stuck is in translating the knowns that I have (centripetal force of 19.6 newtons, tangential speed of 12,607.506 meters/second) into something I can determine radius with. I always seem to be one unknown short. If I knew the orbital period, it would be trivial to get the radius, knowing that it travels 2π radians in a full rotation.

First of all, are my assumptions correct? Any hints are very welcome. I feel like its some little thing I'm missing that will make all of the pieces come together :)