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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.

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

Kepler s

Universal Gravitation

UCM ?

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

[itex]

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

[/itex]

Could I use the uniform circular motion equation [itex]F_c= \frac{mv^2}{r}[/itex] 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 [itex]v[/itex], but if I could use it in this situation, what would I use as [itex]r[/itex], 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,

1. Homework Statement1. 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.

**2. Homework 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,

[itex]

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

[/itex]

Could I use the uniform circular motion equation [itex]F_c= \frac{mv^2}{r}[/itex] 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 [itex]v[/itex], but if I could use it in this situation, what would I use as [itex]r[/itex], 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,

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