Question

On october 15, 2001, a planet was discovered orbiting around the star hd 68988. its orbital distance was measured to be 10.5 million kilometers from the center of the star, and its orbital period was estimated at 6.3 days. what is the mass of hd 68988? express your answer in kilograms and in terms of our sun's mass.

Answer 1

The mass of sun is equal to 1.99 x 10^30 kg. The calculated mass of sta HD68988 is 2.3 x 10^30 kg. The mass of the star is,

M = (2.3 x 10^30 kg) * (1 M / 1.99 x 10^30 kg) = 1.16M.

Therefore, the mass of HD68988 is 1.16M

 

Answer 2

The mass of the star hd 68988 is about 2.3 × 10³⁰ kg.

The mass of the star hd 68988 is about 1.16 times of our sun's mass.

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Further explanation

Centripetal Acceleration can be formulated as follows:

$\large {\boxed {a = \frac{ v^2 } { R } }$

a = Centripetal Acceleration ( m/s² )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

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Centripetal Force can be formulated as follows:

$\large {\boxed {F = m \frac{ v^2 } { R } }$

F = Centripetal Force ( m/s² )

m = mass of Particle ( kg )

v = Tangential Speed of Particle ( m/s )

R = Radius of Circular Motion ( m )

Let us now tackle the problem !

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Given:

mass of the sun = M_sun = 1.99 × 10³⁰ kg

radius of the orbit = R = 10.5 × 10⁶ km = 1.05 × 10¹⁰ m

Orbital Period of planet = T = 6.3 days = 6.3 × 24 × 3600 = 544320 seconds

Unknown:

mass of the star = M = ?

Solution:

Firstly , we will use this following formula to find the orbital period:

$F = ma$

$G \frac{ Mm}{R^2}=m \omega^2 R$

$G M = \omega^2 R^3$

$\frac{GM}{R^3} = \omega^2$

$\omega = \sqrt{ \frac{GM}{R^3}}$

$\frac{2\pi}{T} = \sqrt{ \frac{GM}{R^3}}$

$M = \frac{4 \pi^2 R^3}{GT^2}$

$M = \frac{4 \pi^2 (1.05 \times 10^{10})^3}{6.67 \times 10^{-11} \times 544320^2}$

$\boxed {M \approx 2.3 \times 10^{30} \texttt{ kg} }$

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$M : M_{sun} = 2.3 \times 10^{30} : 1.99 \times 10^{30}$

$M : M_{sun} \approx 1.16$

$\boxed {M \approx 1.16 \times M_{sun}}$

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441

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Answer details

Grade: High School

Subject: Physics

Chapter: Circular Motion