A planet orbits a star at a distance of 3.0 × 10^7 m - Scottish Highers Physics - Question 5 - 2016
Question 5
A planet orbits a star at a distance of 3.0 × 10^7 m.
The star exerts a gravitational force of 1.6 × 10^7 N on the planet.
The mass of the star is 6.0 × 10^30 kg.
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Worked Solution & Example Answer:A planet orbits a star at a distance of 3.0 × 10^7 m - Scottish Highers Physics - Question 5 - 2016
Step 1
Step 1: Use the formula for gravitational force
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Answer
The gravitational force between two masses is given by the formula:
F=Gr2m1m2
where:
F is the gravitational force,
G is the gravitational constant (6.674×10−11N m2/kg2),
m1 and m2 are the masses of the two objects,
r is the distance between the centers of the two masses.
In this case, m1 is the mass of the star (6.0×1030kg), m2 is the mass of the planet (which we need to find), and r is the distance (3.0×107m).
Step 2
Step 2: Rearrange the formula to find the mass of the planet
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Answer
Rearranging the formula gives:
m2=Gm1Fr2
Substituting in the known values:
F=1.6×107N,
r=3.0×107m,
G=6.674×10−11N m2/kg2,
m1=6.0×1030kg.
Step 3
Step 3: Calculate the mass of the planet
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Answer
Plugging in the values:
m2=(6.674×10−11)(6.0×1030)(1.6×107)(3.0×107)2
Calculating (3.0×107)2=9.0×1014m2, we have:
m2=(6.674×10−11)(6.0×1030)(1.6×107)(9.0×1014)
Carrying out the calculations, we ultimately find:
m2=3.6×1010kg
So, the answer is C. 3.6 × 10^{10} kg.
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