Question 9 A newly discovered planet, Eagal, has two known moons, Dorainn and Bron. The table below gives some of the known information about Dorainn and Bron. Dorainn Bron Mass 1.427 x 1015 kg 1.427 x 1015 kg Radius 6.142 km Orbital Period 1.091 x 105 s Orbital Radius 23,640 km 27,650 km a. Determine the gravitational field strength at the surface of Dorainn. b. Using only the information provided for each moon and proportionality, determine Bron's orbital period. Clearly show or explain all workings. c. Use the data provided for Dorainn to determine the mass of Eagal. d. Determine the orbital speed of Bron.

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Question 9
A newly discovered planet, Eagal, has two known moons, Dorainn and Bron. The table below
gives some of the known information about Dorainn and Bron.
Dorainn
Bron
Mass
1.427 x 1015 kg
1.427 x 1015 kg
Radius
6.142 km
Orbital Period
1.091 x 105 s
Orbital Radius
23,640 km
27,650 km
a. Determine the gravitational field strength at the surface of Dorainn.
b. Using only the information provided for each moon and proportionality, determine
Bron's orbital period. Clearly show or explain all workings.
c. Use the data provided for Dorainn to determine the mass of Eagal.
d. Determine the orbital speed of Bron.
Transcribed Image Text:Question 9 A newly discovered planet, Eagal, has two known moons, Dorainn and Bron. The table below gives some of the known information about Dorainn and Bron. Dorainn Bron Mass 1.427 x 1015 kg 1.427 x 1015 kg Radius 6.142 km Orbital Period 1.091 x 105 s Orbital Radius 23,640 km 27,650 km a. Determine the gravitational field strength at the surface of Dorainn. b. Using only the information provided for each moon and proportionality, determine Bron's orbital period. Clearly show or explain all workings. c. Use the data provided for Dorainn to determine the mass of Eagal. d. Determine the orbital speed of Bron.
Expert Solution
Step 1

Given data:

Mass of each moon: m=1.427×1015kg

Radius of Dorainn, rD=6.142 km=6.142×103m

Orbital period of Dorainn, TD=1.091×105s

Orbital radius: RD=23640×103m; RB=27650×103m

 

 

Step 2

To determine:

  1. Gravitational field strength at the surface of Dorainn.
  2. Bron's orbital period.
  3. Mass of Eagal.
  4. Orbital speed of Bron.
Step 3

Explanation:

a.  Gravitational field strength can be calculated as follows:

gD=GmrD2gD=6.67×10-11N.m2/kg21.427×1015kg6.142×103m2gD=2.52×10-3m/s2

b.  Using Kepler's third law, the orbital speed of Bron can be calculated as follows:

T2R3TDTB2=RDRB3TD2RB3=TB2RD3TB=TD2RB3RD3TB=1.091×105s227650×103m327640×103m3TB=1.092×105s

 

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