Centripital VS Gravitational Force

[DocDrakeRamoray]

For example, if there are two satellites of equal mass and orbiting around the Earth with same velocity. How the force holding them in orbit is different if one satellite is twice the distance from the earth. What is the ration of centripital forces?


I thought in terms of Fc= mv^2/r, but the answer was in terms of Fg= Gmm/r^2

Why don't we get the same answer using either formula? Obviously in one case force (Fc) is two times smaller and in the other case (Fg) is 4 times smaller.

Isn't Fc= mv^2/r for centripital force? then twice the distance would mean Fc would be halved. or there has to be a string holding an orbiting object in orbit for this formula to be relavent?

I don't get it, I'm sure there is an easy explanation but I can't find it

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[VanBrown]

because gravity doesn't require a velocity. in the question it says they are the same mass and velocity. so their centripetal force will be 1:2 but their gravitational force will be 1:4.

the force holding anything in orbit is always gravity... centripetal force isn't a force by itself.. it is the result of other forces...

so remember that Fc=ma where a is the acceleration to the tangental velocity... its the force that must exist to keep things in orbit.

 

[DocDrakeRamoray]

because gravity doesn't require a velocity. in the question it says they are the same mass and velocity. so their centripetal force will be 1:2 but their gravitational force will be 1:4.

the force holding anything in orbit is always gravity... centripetal force isn't a force by itself.. it is the result of other forces...

so remember that Fc=ma where a is the acceleration to the tangental velocity... its the force that must exist to keep things in orbit.

That's the thing, the question asked for centripital force, I picked 1/2, but the answer was 1/4..........that's where all the confusion came from

 

[VanBrown]

i dont know... where is this question from? it could just be a bad question.

 

[DocDrakeRamoray]

............

 

[VanBrown]

I must have it backwards then. Gravity is the force between them but it is an attractive force. Maybe gravity says that the two masses should hit each other. Centripetal force seems to be what is keeping them in orbit... without it one of the masses (the orbiting one) would just shoot away from the thing it was orbiting.

 

[amikhchi]

Isn't centripetal force not really a force, it's just a label for the force (whatever type) that causes uniform circular motion?

in that case the gravitational force between the earth/satellite is what creates the centripetal acceleration, and therefore Fc = Fg, so if you double the R you are decreasing the gravitational force by a factor of 4 and same for the Centripetal force giving you a 1:4 ratio

if you think about it, if you have an object in UCM, you can't increase the radius and keep it at the same velocity without changing the force supplying the centripetal acceleration. In this case the force is gravity...

after re-reading what i wrote, i don't know what i'm talking about, i think i'm on the right track, but then again something doesn't seem right, you'd think doubling R would decrease Fc by 2 but Fg by 4, but if Fg is supplying Fc... ehhh, no idea, but i'd like to know if it's just a bad question or what

 

[vickpick]

copy the question exactly as it is written in the book.

 

[EkramVahsedi86]

In two dimensions the angular velocity is a single number which has no direction. For this problem to make sense, you have to work with radians (since velocity is a vector, don't try to use the scalar term, speed, unless the problem says to).

ω = d(theta)/dt

Suppose satellite 1 orbits earth at a rate of 6.28 radians per second from a radius of 40.5 trillion meters

Suppose satellite 2 orbits earth at a rate of 6.28 radians per second from a radius of 81 trillion meters

In one second, satellite 1 travels 2*pi*r meters = 81-trillion-pi
In one second, satellite 2 travels 2*pi*2r meters = 162-trillion-pi

So now satellite 1 has half the SPEED of satellite 2 and you can use the speed formulas.

Satellite 1 has half the speed now, and the answer is finally correct.

The centripetal accceleration
for satellite 1 is 6.561 * 10^21 * pi^2 * m^-1
for satellite 2 is 2.6244 * 10^22 * pi^2 * m^-1

The quotient of sat 1 divided by sat 2 = 0.25