The answer can be found be using the formula of orbital velocity v=√{(G*M)/R}
Here G =Gravitational constant (G=6.67*10^-11 m³ kg⁻¹ s⁻²)
M= Mass of star
R = The distance between planet and the star
As we also know, v=ωR,
Here, ω= angular velocity
R= radius
ωR=√{(G*M)/R}, now, ω=2π/T, where T is the orbital period of the planet
(2π/T)*R=√{(G*M)/R}, we "put to the power of 2" both sides to get rid of the square root and get:
{(2π/T)*R}²=[√{(G*M)/R}]²,
(4π²/T²)*R²=(G*M)/R, we multiply by R:
(4π²/T²)*R³=G*M, now we solve for R and get:
R³=(G*M*T²)/4π², we take the third root to get R:
R=∛{(G*M*T²)/4π²}, inserting the values of time and mass ( T= 2.8 x 10 s and Mass= 6.2x 10 kg)
R=∛{(G*M*T²)/4π²},
R=R=∛[{G=6.67*10^-11 x 6.2x 10 x (2.8 x 10^2)/4x3.14²},
R=9.36*10^11 m
So this will be the average distance between the star and the planet.
Answer:
9.36 * 10^11 m
Explanation:
The formula of general velocity can be used here = v=√{(G*M)/R}.
G = gravitational constant or 6.67*10^-11 m³ kg⁻¹ s⁻²
M = Mass of the star
R = radius
To find v we use the formula v=ωR.
Here ω is the angular velocity; ω = ω=2π/T
Here T is the orbital period of the planet
The formula is arranged likewise: (2π/T)*R=√{(G*M)/R}
Step 2: {(2π/T)*R}²=[√{(G*M)/R}]²
Step 3: (4π²/T²)*R²=(G*M)/R
Step 4: (4π²/T²)*R³=G*M
Step 5: R³=(G*M*T²)/4π²
Step 6: R=∛{(G*M*T²)/4π²}
Step 7: Add your numbers to the formula and we get the answer.
