# Calculating Speed of Asteroid at its Perihelion

In summary, the asteroid has a perihelion at 1AU and an aphelion at 3AU. Its speed at its perihelion is calculated to be 2.98x1011m/s.
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. Homework Statement

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

## Homework Equations

Kepler s
Universal Gravitation
UCM ?

## The Attempt at a Solution

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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 realized, so would appreciate any help.

Thanks,

Last edited:
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.

TSny said:
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.

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.

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

You will need a second conserved quantity.

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

You will need a second conserved quantity.

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.

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?

TSny said:
The Earth is not relevant to this question. You just have the asteroid orbiting the sun.

See if this link helps refresh your memory concerning orbital angular momentum: http://hyperphysics.phy-astr.gsu.edu/hbase/amom.html

Thanks for the link. I didn't think I could, I just couldn't think what else, as it's not like it has any moons (the only question i did before with regarding the Earth Moon system.

gneill said:
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?

Nothing until now, did not know there was a link. But after doing a quick google search I found this http://en.wikipedia.org/wiki/Vis-viva_equation , thanks!

## 1. What is the formula for calculating the speed of an asteroid at its perihelion?

The formula for calculating the speed of an asteroid at its perihelion is: Speed = (2π * Semi-Major Axis) / Time Period, where the semi-major axis is the distance from the center of the asteroid's orbit to its closest point to the sun (perihelion) and the time period is the time it takes for the asteroid to complete one full orbit.

## 2. How do you determine the semi-major axis of an asteroid's orbit?

The semi-major axis of an asteroid's orbit can be determined by measuring the distance from the center of the asteroid's orbit to its closest point to the sun (perihelion) and its farthest point from the sun (aphelion) and then dividing that distance by 2.

## 3. What unit of measurement is typically used for the speed of an asteroid?

The speed of an asteroid is typically measured in kilometers per second (km/s) or miles per hour (mph).

## 4. How does the speed of an asteroid at its perihelion compare to its speed at its aphelion?

The speed of an asteroid at its perihelion is usually faster than its speed at its aphelion. This is because the asteroid is closer to the sun at its perihelion, which causes it to experience a stronger gravitational pull and therefore move faster.

## 5. Why is it important to calculate the speed of an asteroid at its perihelion?

Calculating the speed of an asteroid at its perihelion can help scientists understand the asteroid's orbit and make predictions about its future movements. It can also provide valuable information about the asteroid's composition and potential hazards it may pose to Earth.

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