Question

The following table gives the mean velocity of planets in their orbits versus their mean distance from the sun. Note that 1 AU (astronomical unit) is the mean distance from Earth to the sun, about 93 million miles.

Planet	d = distance (AU)	v = velocity (km/sec)
Mercury	0.39	47.4
Venus	0.72	35.0
Earth	1	29.8
Mars	1.52	24.1
Jupiter	5.20	13.1
Saturn	9.58	9.7
Uranus	19.20	6.8
Neptune	30.05	5.4

Astronomers tell us that it is reasonable to model these data with a power function.

(a)

Use power regression to express velocity as a power function of distance from the sun. (Round regression parameters to two decimal places.)

v = 29.73 × d^0.50

v = 21.41 × d^−0.50

    

v = 29.73 × d^−0.73

v = 29.73 × d^−0.50

v = 21.41 × d^−0.29

(b)

Plot the data along with the regression equation.

(c)

An asteroid orbits at a mean distance of 3 AU from the sun. According to the power model you found in part (a), what is the mean orbital velocity of the asteroid? (Round your answer to two decimal places.)

_______ km/sec

Answer 1

Hey first you need to transform your model into log and then use linear regression technique. I have used excel you may use you calculator as it already has power regression.

in the image above yellow highlighted table has estimated coefficients and the graph has raw data as orange dots and fitted line .

Below is some handwritten manipulation you might need-

these are table value if you need-

Planet	d = distance (AU)	v = velocity (km/sec)	ln(d)	ln(v)	fitted data
Mercury	0.39	47.4	-0.94160854	3.85862223	47.60610013
Venus	0.72	35	-0.32850407	3.55534806	35.03714101
Earth	1	29.8	0	3.39450839	29.73
Mars	1.52	24.1	0.418710335	3.18221184	24.11421425
Jupiter	5.2	13.1	1.648658626	2.57261223	13.03746746
Saturn	9.58	9.7	2.259677592	2.27212589	9.605327006
Uranus	19.2	6.8	2.954910279	1.91692261	6.784913181
Neptune	30.05	5.4	3.402862661	1.68639895	5.423412916

after getting log data goto data tab and select regression then select y values as your velocity values and x values as distance value and click ok you will get th estimated values.

Please upvote If I am able to help you.

Thanks