# Calculating Speed of Asteroid at its Perihelion

1. May 27, 2015

This is not part of my coursework; I am preparing for an exam and this is a question from a past paper to which answers are not given.

1. The problem statement, all variables and given/known data

An asteroid orbiting the sun has its perihelion at 1AU and its aphelion at 3AU. Calculate the speed of the asteroid at its Perihelion.

2. Relevant equations
Kepler s
Universal Gravitation
UCM ?
3. The attempt at a solution

I am a bit stuck on this. First I calculated its semi-major axis as I assume it will be needed,

$a=\frac{r_a + r_b}{2}=\frac{(1.49 \times 10^{11})+(3 \times 1.49 \times10^{11}}{2} = 2.98 \times 10^{11} m$

Could I use the uniform circular motion equation $F_c= \frac{mv^2}{r}$ in this situation? I ask as its an a moderately eccentric ellipse.

I was thinking of equating that to the force of gravity to get $v$, but if I could use it in this situation, what would I use as $r$, the semi-major axis, or 1AU?

If I cannot use that UCM equation then I am more stuck than I realised, so would appreciate any help.

Thanks,

Last edited: May 27, 2015
2. May 27, 2015

### TSny

Since the motion is not UCM, then you would need to justify using the UCM equation with the semi-major axis. I'm pretty sure it won't lead to the right result.

Can you think of a couple of quantities that are conserved in the orbital motion?

What units are you using for distance? The 1015 factors look strange to me.

3. May 27, 2015

Sorry, I remembered incorrectly, it is 1011 in metres.

Angular momentum? But I cannot see how I can work with that, not knowing the asteroids shape etc.

4. May 27, 2015

### TSny

Orbital angular momentum is conserved. Treat the asteroid as a point particle.

You will need a second conserved quantity.

5. May 27, 2015

Ok thanks. Have not done many problems in angular momentum, could I use the Earth?

EDIT: Typo in op, the aphelion is 3AU, not 2.

6. May 27, 2015

### TSny

7. May 27, 2015

### Staff: Mentor

Hi FaraDazed. If I might offer a hint: what do you know about the relationship between the semi-major axis of an orbit and its specific mechanical energy?

8. May 27, 2015