# Planetary motion

1. Dec 8, 2005

### fahd

hi i hv these 2 doubts....i tried using the elliptic equation:
r= a(1-e^2)/[1-e cos(theta)] however i cant really figure out how do i determine the answer,,i mean if i could know what exactly to do.

1) the orbit of venus is very near circular (e=0.0068).Assuming that the orbit is completely circular, what wud be the orbital motion of Venus if the mass of the sun were to suddenly drop by a factor of two?Would Venus be able to remain in the solar sysytem?if so at what radius cud it be found?

2)A satellite moves in an elliptic orbit with e= 0.5 around a planet from which it is launched.When it arrives at an apsis (a radial turning point),its velocity is suddenyl doubled .Show that the new orbit will be either paraboloc or hyperbolic according to which of the turning points the velocity doubling occurs?

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i really wanna know how to do these so that i can apply similar concepts to solve the other questions too..
also another quick question....given 'r' describing the motion of a planet in ,how can i find the speed?
thanks.

2. Dec 8, 2005

### QuantumDefect

The first one you start with Conservation of energy. You can find the kinetic energy by using Centripetal acceleration. Once you know that, you plug it in to your Cons. of Energy. Equation. Then you look look at the potential energy term. You know that if the mass of the sun drops suddenly to half of its origional value, then the potential energy changes specifically M_sun ---> .5M_Sun. Youll find that the total energy goes to zero! And because its zero, it goes into a parabolic orbit.
You can find the speed at a particular point in the orbit by using conservation of angular momentum if you have a velocity at some point. Or you could differentiate with respect to time, your orbit equation
As for your next question ill have to think about it for awhile. Hope this helps

Last edited: Dec 8, 2005
3. Dec 8, 2005

### emptymaximum

they can both be solved in the same manner. when dealing with conic section remember that the eccentricity $\epsilon$ is what determines the form of the conic. If $\epsilon \geq 1$ then the orbit will not be a closed path. recall:
$$\epsilon = \sqrt{1 + E \frac{2 m { \ell }^2} {k^2}}$$
where k is the constant from the potential energy function (2GMm), and $\ell = | \vec{r} \times \vec{v} |$

also, in your problem two, an apsis isn't a 'turning point' as the particle does not reverse motion.
an apsis is where r has a maximum/minimum value, which correspong to the perihilion and aphelion.

Last edited: Dec 8, 2005
4. Dec 8, 2005

### fahd

thanks

thanks a lot for all ur help...
ill make sure i apply this concept to the other questions as well..
thanks again!

5. Dec 8, 2005

### fahd

a quick question..dun u think. the constant K shud be GMm instead of
2GMm.
thanks

6. Dec 9, 2005

### emptymaximum

yup.
don't know why i put a 2 there.
sorry.
/s

7. Dec 9, 2005

### fahd

2)A satellite moves in an elliptic orbit with e= 0.5 around a planet from which it is launched.When it arrives at an apsis (a radial turning point),its velocity is suddenyl doubled .Show that the new orbit will be either paraboloc or hyperbolic according to which of the turning points the velocity doubling occurs?

i am not quite knowing hw to do this question..tried all stuff..but always contradicts facts..i used the equation for mechanicsla energy conservation and then tried to state that fopr parabolic or hyperbolic motion, e has to be =0 and >0 respectively...however for the parabolic path its ok but its contradicting my answer for the hperbolic type
can sumone help with sum other method??
thanks......:(

Last edited: Dec 9, 2005
8. Dec 9, 2005

### emptymaximum

no
$\epsilon = 1$ for parabolic orbit, and > 1 for hyperbolic
when $\epsilon = 0$ , it is circular orbit and when $$0 < \epsilon < 1$$ it is elliptical.