Multiple Choice) two starts orbit due to the gravitational force of one star upo

Question

Multiple Choice) two starts orbit due to the gravitational force of one star upon the other. Star A has mass Ma, its orbit is uniform circular, it's orbital center is the (stationary) origin of the coordinate system, and it's orbital radius is Ra. Star B has mass Ma/4. There are no other stars within light-years of the two.

Problem1) What can be said about the magnitude of the forces on the stars, Fa and Fb?

A) Fa = Fb/4

B) Fa = Fb/2

C) Fa = Fb

D) Fa = 2*Fb

E) Fa = 4*Fb

-----

Problem2) in problem 1, what must Fa point toward?

A) Star B

B) Star A's orbital center

C) Neither

D) Both

E) we don't have sufficient information.

----

Problem3) in problem1, which relation between the two orbital radiuses is valid?

A) Rb=Ra/4 (Mb/Rb = Ma/Ra)

B) Rb=Ra/2 (Mb/Rb^2 = Ma/Ra^2)

C) Rb=Ra

D) Rb=2*Ra (Mb*Rb^2 = Ma*Ra^2)

E) Rb=4*Ra (Rb*Mb = Ra*Ma)

-------

Problem4) in problem1, which is the correct F=ma equation for Star A. (Va=orbital speed)

A) GMaMb/Ra^2 = MaVa^2/Ra

B) GMaMb/(Ra^2 + Rb^2) = MaVa^2/Ra

C) GMaMb/(Ra+Rb)^2 = MaVa^2/Ra

D) GMaMb/(Ra^2 + Rb^2) = MaVa^2/(Ra+Rb)

E)GMaMb/(Ra+Rb)^2 = MaVa^2/(Ra+Rb)

-----

Problem5) in problem1, suppose Ra + Rb = 1.5*10^12 meters. What is Ra?

A) 1.20*10^12 meters

B) 1.00*10^12 meters

C) 0.75*10^12 meters

D) 0.50*10^12 meters

E) 0.30*10^12 meters

----

Problem 6) in Problem1, what is the expression for Va^2?

A) GMb/Ra

B) GMb/5Ra

C)GMb/25Ra

D) 3GMb/5Ra

E) GMb/(Ra+Rb)

----

Problem7: in problem 1, suppose (GMb=0.25*10^20 m^3/s^2) what is Va?

A) 1830 m/s

B) 3160 m/s

C) 4080 m/s

D) 5480 m/s

E) 5770 m/s

----

Problem8) in Problem1, how much apporximately is the orbital period?

A) 10 earth years

B) 25 earth years

C) 33 earth years

D) 47 earth years

E) 55 earth years

Explanation / Answer

1) the force of gravitation for both the stars is same

option c

2) the force is excerted on the planet B

option a

3) Fa = Fb

Gm1m3/r1^2 = Gm2m3/r2^2

Ma/ra^2 = Mb/rb^2

Ma/ra^2 = Ma/4*rb^2

4*rb^2 = ra^2

ra = 2*rb

rb = ra/2

option b

4) considering only planet A

GMaMb/Ra^2 = MaVa^2/Ra

option a

5) Ra + Rb = 1.5x10^12

Ra + Ra/2 = 1.5x10^12

3Ra/2 = 1.5x10^12

Ra = 1x10^12 m

option b

6) Va^2 = G*Mb/(Ra+Rb)

option e

7) Va = sqrt(G*Mb/(Ra+Rb))

Va = 4082.5 m/s

option c

8) T = 2pisqrt(a^3/G*M)

T = pi*sqrt(1x10^12)^3/0.25x10^20*4)

T = 3.14x10^8 s

T = 10 eart years

option a

Related Questions

Navigate

• Browse (All)
• Browse M
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.