Is There Any Torque Acting on a Satellite in an Elliptical Orbit?

[fredrick08]

Rotational Kinematics, Challenge!

Homework Statement

A satellite follows an elliptical orbit. The only force on the satellite is the gravity atraction from the planet. The satellites speed at point A is 8000m/s, and it is 6000km away, Point B is 24000km east of the planet, and Point C is component vector 9000ikm+12000jkm away, if the you take the planet as the origin.

a. Is there any torque acting on the satellite?
b. satellite speed at Point B
c, satellite speed at Point C

Homework Equations

We have just started rotational kinematics, and have not yet done space physics like Newtons constant of gravity and that stuff. So just Lf=Li, conservation of momentum.

The Attempt at a Solution

a. i supect there is no torque because there is no external force acting on the satellite, as the gravity act as the moment arm.
b and c. i used La=Lb=Lc, therefore RaVa=RbRb=RcVc,
therefore giving Vb=(RaVa)/Rb and Vc=(RaVa)/Rc, and that Rc=sqrt(9000^2+12000^2)=15000, so my answers i get are 2000m/s at point B and 3200m/s at Point C, but the answers in the book say 2000m/s and 4000m/s... so can someone please tell me where i have gone wrong? TY

 

[Dick]

Let's just start with a). Your answer is completely vague and wrong. What's an actual expression that will let you compute the torque and using that, say why you think it would be constant.

 

[fredrick08]

ok, as torque=rFsin(theta), since there is no Force, then there is no torque, is that better?

 

[fredrick08]

ok, i have thought about it a bit more, and is my answer wrong because i have ignored the angle? therefore RaVaSin(90)=RbVbSin(90)=RcVcSin(12000/9000) this gives the answer in the book, but is it correct, in the way it meant to be done?

 

[ok123jump]

fredrick08,

Yes, you have the correct answers in your 3rd post. Note that $$sin(90) = sin(\pi/2)= 1$$.

To answer why you were incorrect for the first part - recall that the Earth is curved and Newton's First Law tells us that the satellite should fly into space except that there is the force of gravity from the earth. Since the Earth diverges from it's tangent, there exists a small angle between the curved path and the satellites path, this is the angle you missed. Hence, $$rFsin(\theta)\neq 0$$ which means there does exist some amount of torque.

 

[fredrick08]

ok, sweet TY, but are you saying that for a) there is torque? because the answer says there's not. and when i look at every diagram i have for toque, there is always a Force acting at an angle, to rotate an object, but in this case there is not...?

 

[fredrick08]

i understand what you mean, and I am not saying your wrong, but its only 1st year physics, so i think the book ignores it... but I am not sure...

 

[Dick]

ok, sweet TY, but are you saying that for a) there is torque? because the answer says there's not. and when i look at every diagram i have for toque, there is always a Force acting at an angle, to rotate an object, but in this case there is not...?

There is no torque, not because there is no force, but because the gravitational force points along the same direction as the vector to the axis of rotation. In torque=Frsin(theta), the theta is 0.

 

[ok123jump]

Ah, you're right, my mistake.

Fredrick08, please ignore my answer =).