Carol Decker Mocvember 3.4, 2159

55 Cancri Extrasolar Planet Confirmation

Objective: To determine if the recently discovered object, tentatively called 55 Cancri g, is a possible exoplanet orbiting 55 Cancri.

Hypothesis: It seems likely that 55 Cancri g is an exoplanet, as it would be difficult to collect the required amount of data for another object.

The formula that is the basis of this lab is... T 2 K = r3 K = Kepler's Constant (d2/AU3) T = period of orbit (d) r = mean orbital radius (AU)

Equipment: Not Applicable

Procedure: Not Applicable

Pre-Lab Questions: None Assigned

Observations:

Exoplanet Period of Orbit (d) Mean Orbital Radius (AU) 55 Cancri b 14.66 0.118 55 Cancri c 44.28 0.240 55 Cancri d 5360 5.90 55 Cancri e 3.00 0.0400 55 Cancri f 260.8 0.738 55 Cancri g* 24.0 0.190 *Unconfirmed planet Analysis: In order to obtain a linear graph, the values of the period of orbit were squared, while the mean orbital radius values were cubed. The following is a graph of period of orbit squared as a function of mean orbital radius for the five confirmed exoplanets in the 55 Cancri system.

Period of Orbit Squared as a function of Mean Orbital Radius Cubed

35000000 f(x) = 139871.5x + 2947.72

30000000

25000000

)

2

^

d

(

d

e

r 20000000

a

u

q

S

t

i

b r 15000000

O

f

o

d

o

i

r

e 10000000

P

5000000

0 0 50 100 150 200 250

Mean Orbital Radius Cubed (AU^3)

The slope is equal to the accepted value of Kepler's constant for the 55 Cancri system since... rise T 2 slope= = =K run r3

This means that from the analysis of the graph we have an accepted value for Kepler's constant of 1.40e5 d2/AU3.

The value of Kepler's constant calculated from the available data on 55 Cancri g is... T 2 24.02 K = = =83977.26=8.40e4 d 2 / AU 3 r3 0.1903

Error: measured−accepted 83977.26−139871.5 % error= = =−0.39961=−40.0 % accepted 139871.5 Conclusion: Based on the available data, it seems very unlikely that 55 Cancri g is a possible exoplanet in the 55 Cancri system. The orbit of 55 Cancri g is simply impossible since the accepted Kepler's constant for the 55 Cancri system is 1.40e5 d2/AU3, while 55 Cancri g has a value of 8.40e4 d2/AU3 (a 40.0% error). Although it seems unlikely, there may have been a significant error in measurements of 55 Cancri g. For this reason it would seem to be advisable that one of the other projects could try to verify the values that were obtained for this questionable exoplanet.