# Homework Help: Why do the centripetal and gravitational force equal each other in orbit?Also

1. Oct 19, 2011

### MakeItThrough

Why do the centripetal and gravitational force equal each other in orbit??Also...

1. The problem statement, all variables and given/known data
Say for example, a problem wants us to find the mass of a planet. It gives us a satellite that orbits that planet with a radius of R and a period T. Now, I know how to solve this problem. You must set Fc = Fg.
But what I do not know is why the centripetal and gravitational force of these two objects must equal each other.

Also, a similar problem to that is one like this:
When you take your 1200 kg car out for a spin, you go around a corner of radius 57.6 m with a speed of 15.2 m/s. The coefficient of static friction between the car and the road is 0.84. Assuming your car doesn't skid, what is the force exerted on it by static friction?

Again, I already know how to solve this. You must set Fc = Ff ... mv^2 / r = Ff, and then you just plug in the given values into the mv^2 / r and that is your answer.
I do not know why in this case the centripetal force and the static friction must equal each other.

If someone could please explain this to me, I would feel so much better while taking the test tomorrow... My teacher goes through this stuff extremely fast.

2. Relevant equations

V = 2piR / T
Fc = mv^2 / r
Fg = Gm1m2 / r^2

2. Oct 19, 2011

### Mindscrape

Re: Why do the centripetal and gravitational force equal each other in orbit??Also...

Newtons second law, sum of forces equals mass times acceleration. The force you have is gravity, and the acceleration is centripetal acceleration.

3. Oct 19, 2011

### PeterO

Re: Why do the centripetal and gravitational force equal each other in orbit??Also...

Simplest acceleration is this:

The gravitational force is the ONLY force acting on the Satellite.

The Centripetal force is the force we would need to have if the satellite is to travel in a circular path.

The satellite DOES travel in a circular path, so the Graitaional force existing happily equals the centripetal force we need.

Gravtational force is a real force.

Centripetal force is a desired/necessary force.

Another example:

Why CAN'T you ride a motorbike in a circle of radius 10m at 150 km/h on flat ground?

Simple, you could calculate the centripetal force NEEDED for that to happen, but when you add up [as vectors] all the forces acting - gravity, reaction force, friction,... They just don't add up to the necessary force, so the situation just can't happen.

In the case of a satellite, the available force [gravity] happens to provide the required force, so its circular motion is maintained.

EDIT: Oh, and in the case of the car - it must have been on flat ground also. Most roads have a small degree of banking so that would have contributed, and if the banking was steep enough - like at a velodrome - you mightn't need friction at all.