an object is orbiting a planet with orbital will speed v, if the radius is same and mass is increased 4 times, by what factor orbital speed will change
Answers
Answer:
An orbit is a fall, plus enough sideways velocity to miss the planet.
Newton established that things fall vertically at the same speed in a vacuum, regardless of whether they are feathers or hammers. This was demonstrated on the moon.
So we know the vertical component will be unchanged: it will continue falling just as fast.
If it is falling just as fast, then the time it would take to hit the ground will be the same, so the sideways velocity it needs to miss the ground in that time will also be the same.
So, changing the mass won't measurably affect the orbital velocity, so long as it it significantly smaller than the planet.
Once it starts weighing a significant proportion of the mass of the planet, then it stops orbiting the planet, and instead orbits the barycenter of the system (“the center of mass”, to a first approximation, though not).
At that point, quadrupling the mass of either object will shift the barycenter, which will change the effective orbital radius, which will change the orbital period.
And then there's the relativistic effects, which is where we start asking whose reference frame you are talking about: a stationary observer, someone on one of the planets…?
Explanation: