1. Imagine that the star Altair has a system of three planets: Betazed, Charybdi

Question

1. Imagine that the star Altair has a system of three planets: Betazed, Charybdis a. Which of Kepler's Laws would you use to determine the length of a year and Deneb on each planet? (1 point b. Assume that the orbits of Charybdis and Deneb have semi-major axes of 2 AU and 3.5 AU, respectively. Which planet travels more rapidly along its orbit? (1 point) The central star of this system has a mass of 1.2 solar masses. If Betazed has a semi-major axis of 1 AU, how long is one year on Betazed? Hint. Refer to Newton's modification of Kepler's Third Law. (2 points) c. 2. A softball pitcher throws a fastball with a force of 800 Newtons. a. If the ball has a mass of 0.8 kg, what is the acceleration experienced by the ball? (1 point)

Explanation / Answer

1) a- I would use the kepler's third law or the harmonic law to determine the length of a year on each planet because this law states the time the planet takes to complete one orbit around the sun from its mean distance.

mathematically, the law says P2=a3 ,where P= time period to orbit around the sun

a= semi major axis of the planet's orbit.

b) its the Charybdis planet which will travel more rapidly along its orbit.

this is so, because time period is directly proportional to the semi major axis and by the third law we can say that

P2=a3 , and thus P=a3/2 , so the planet which has less semi major axis will travel at a faster rate or its time period will be less compared to one which has larger semi major axis , in this case in b- Charybdis has a=2 AU and Deneb= 3.5 AU

so according to law Charybdis will travel faster along the orbit.

2) given ;

mass= 0.8 kg , F=800 N

and F= m.a

so, a= F/m= 800/0.8

=100 m/s2

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