Circular Motion – Orbital Mechanics

1. The problem statement, all variables and given/known data

Question 1. If two objects were in the same orbit around a planet they would both have the same orbital velocity regardless of their mass. Using the equation given, explain why an object with twice the mass experiences the same orbital velocity.

2. Relevant equations

Centripetal force = mv^2/r

3. The attempt at a solution

I know it has something to do with gravitational forces being proportional to mass but I am unsure how to relate it to the equation. If the object was twice as massive then it would experience twice the centripetal force which I thought would tend to increase the velocity?

I have seen other sources say things about planets/objects in orbit ‘fall’ like objects on Earth but wouldn’t the velocity related to falling objects on Earth be different to the velocity of objects in orbit as their velocity is tangential which isn’t influenced by gravity?

Any help is much appreciated! 🙂

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