What is the mass of 55 Cancri in kg and solar masses?

[Lauren0619]

Homework Statement

I have to find the mass of 55 Cancri in kg using the average orbits of 3 orbiting planets. Specifically, "Using the average of the values of R^3/T^2 that you filled in just for planets c, f, and d in #2, approximately what is the mass of 55 Cancri in kg?
planet c = 3.14 x 10^18
planet f = 3.16 x 10^18
planet d = 3.10 x 10^18

Then to convert the mass in kg to solar masses.

Homework Equations

M=(4pi^2/G)(R^3/T^2) With T equaling the period

The Attempt at a Solution

(3.14 x 10^18) + (3.16 x 10^18) + (3.10 x 10^18) / 3 = 7.3 x 10^31
M= (4pi^2/6.67x10^11)(7.3x10^18) = 1.73x10^31 kg

Is this correct? Or is this value in another form that I need to convert to kg?

And then would it convert to 8.70 Ms (solar masses)?

Please help! Thank you all!

 

[gneill]

All of your data values are close to 3 x 10¹⁸, so I would expect their average to be similar. Check your average calculation.

 

[Lauren0619]

All of your data values are close to 3 x 10¹⁸, so I would expect their average to be similar. Check your average calculation.

Thanks gneill! I redid the calculations. You were right. For my average I got 3.13x10^18. I plugged that into the formula to calculate mass and got 1.85x10^30 kg. Is this correct?

 

[gneill]

Yes, that looks much better.

 

[Lauren0619]

Yes, that looks much better.

Cool! And just to be sure, this is in kilograms, right? I wasn't sure if there was a conversion that I needed to do that was missing.

Also, I redid the conversion to solar masses from kilograms and got .93Ms.

 

[gneill]

Cool! And just to be sure, this is in kilograms, right? I wasn't sure if there was a conversion that I needed to do that was missing.

Your problem statement didn't mention what units the R^3/T^2 values were given in so I can't say decisively, but it would make sense that they'd be in $m^3/s^2$, giving you a result in kg.

Also, I redid the conversion to solar masses from kilograms and got .93Ms.

That looks reasonable.