Physics, 21.06.2019 20:20 vero5047

Astronomers discover an exoplanet (a planet of a star other than the sun) that has an orbital period of 3.87 earth years in its circular orbit around its sun, which is a star with a measured mass of 3.59 x 1030 kg. find the radius of the exoplanet's orbit.

Answers: 3

Show answers

Answers

Answer from: calebcoolbeans6691

Given the orbital period and mass of the exoplanet, its radius of orbit is 4.488 × 10¹¹m.

Given the data in the question;

Orbital period; $T = 3.87 \ Earth\ years = [ 3.87yrs*365days*24hrs*60min*60sec = 122044320s$ Mass of the Planet; $M = 3.59*10^{30}kg$ Radius of the exoplanet's orbit; $r= \ ?$

To determine the radius of the exoplanet's orbit, we use the equation from Kepler's Third Law:

$T^2 = \frac{4\pi^2 }{GM}r^3\\$

Where, T is the period of the orbit of the exoplanet, G is the Gravitational Constant, M is the mass of the star and r is orbital radius.

We make "r", the subject of the formula

$r = \sqrt[3]{\frac{T^2GM}{4\pi ^2} }$

We substitute our given values into the equation

$r = \sqrt[3]{\frac{(122044320s)^2*(6.67430 * 10^{-11} m^3/kg s^2)*(3.59*10^{30}kg)}{4*\pi ^2} } \\\\r = \sqrt[3]{\frac{(1.48948*10^{16}s^2)*(6.67430 * 10^{-11} m^3/kg s^2)*(3.59*10^{30}kg)}{4*\pi ^2} }\\\\r = \sqrt[3]{\frac{3.5689*10^{36}m^3}{4*\pi ^2} }\\\\r = \sqrt[3]{9.04*10^{34}m^3}\\\\r = 4.488*10^{11}m$

Therefore, given the orbital period and mass of the exoplanet, its radius of orbit is 4.488 × 10¹¹m.

Learn more; link

Answer from: spinshot13

$4.487(10)^{11}m$

Explanation:

This problem can be solved using the Third Kepler’s Law of Planetary motion:

“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”.

This law states a relation between the orbital period of a body (the exoplanet in this case) orbiting a greater body in space (the star in this case) with the size of its orbit:

$T^{2}=\frac{4\pi^{2}}{GM}a^{3}$ (1)

Where:

T=3.87Earth-years=122044320s is the period of the orbit of the exoplanet (considering 1Earth-year=365days )

is the Gravitational Constant and its value is $6.674(10)^{-11}\frac{m^{3}}{kgs^{2}}$

$M=3.59(10)^{30}kg$ is the mass of the star

is orbital radius of the orbit the exoplanet describes around its star.

Now, if we want to find the radius, we have to rewrite (1) as:

$a=\sqrt[3]{\frac{T^{2}GM}{4\pi^{2}}}$ (2)

$a=\sqrt[3]{\frac{(122044320s)^{2}(6.674(10)^{-11}\frac{m^{3}}{kgs^{2}})(3.59(10)^{30}kg)}{4\pi^{2}}}$ (3)

Finally:

$a=4.487(10)^{11}m$ This is the radius of the exoplanet's orbit

Answer from: Quest

hello, i am papaguy.

i have found an answer to your question but use it as information.

information: because weak acids/bases have low concentration of hydrogen ions, the addition of water has a large impact on the ph. 2. a difference in 1 unit is a 10x difference in concentration for example; a liquid with ph of 3 is 10x more acidic than a liquid with a ph of 4. therefore, a liquid with a ph of 3 is stronger.

best of luck!

Answer from: Quest

Gas will most likely fill the container

Another question on Physics

Physics, 22.06.2019 08:00

1.what is where an object is located 2. what is how fast an objects speed is changing 3. what is how fast an object is moving

Answers: 1

Answer

Physics, 22.06.2019 17:50

Convection occurs when thermal energy is transferred by the movement of

Answers: 1

Answer

Physics, 22.06.2019 18:00

Astudent weighing 700 n climbs at constant speed to the top of an 8 m vertical rope in 10 s. the average power expended by the student to overcome gravity is most nearly

Answers: 2

Answer

Physics, 22.06.2019 20:00

Aspectroscope breaks light up into its colors, allowing scientists to analyze light from the solar system and universe. by studying the spectral line patterns, widths, strengths and positions, scientists can determine the speed, position, and of celestial bodies. a) age b) origin c) rotation d) temperature

Answers: 1

Answer

You know the right answer?

Astronomers discover an exoplanet (a planet of a star other than the sun) that has an orbital period...

Questions

Engineering, 21.05.2020 23:08

I need a 300 word essay about why its a good idea to join a automotive college class...