Calculating the Semimajor Axis of Pasachoff's Orbit

[tnutty]

Homework Statement

The asteroid Pasachoff orbits the Sun with a period of 1417 days.

What is the semimajor axis of its orbit? Determine from Kepler's third law, using Earth's orbital radius and period, respectively, as your units of distance and time.

ans : _______ km

Homework Equations

T^2 = (4(pi^2) r^3) / GM

The Attempt at a Solution

1417 days -> 122428800

(122428800)^2 = 4*pi^2 (r^3) / GM

r^3 = (122428800 GM )/ (pi^2*4)

r^3 ~ 4.116 x 10^26

r ~ 7.429 * 10^8 km

I don't know is this right?

I used M = mass of the sun = 1.99*10^30.
G = 6.67 * 10^-11

 

[Kurdt]

Where have you used the values for the Earth's orbit in your attempt? This should give you the clue as to what you should be doing. You know that Kepler's law states that the period squared is proportional to the semimajor axis cubed. If you already have the data for one orbit you can find the unknown of another by dividing both proportionalities.

 

[D H]

That's not the correct answer, and you didn't use Kepler's third law. Kepler's third law is

$$T_{planet}^2 \propto a_{planet}^3$$

or

$$\frac{a_{planet}^3}{T_{planet}^2} = \text{constant}$$

Use this in conjunction with the fact that the Earth orbits the Sun in 1 sidereal year at 1 AU.