Determine the orbital period for an object orbiting at a distance of 7.3x10^8 from the center of a spherical object whose mass is 3.0x10^27 at a velocity of 2.8x10^4.

Answers

Answer 1

The orbital period for an object can be determined using Kepler's third law of planetary motion, which states that the square of the orbital period is proportional to the cube of the average distance from the center of the spherical object.

To calculate the orbital period, we can use the formula:

[tex]T^2 = (4π^2 / G * M) * r^3[/tex]
Where T is the orbital period, G is the gravitational constant[tex](6.67430 × 10^-11 m^3 kg^-1 s^-2)[/tex], M is the mass of the spherical object, and r is the distance from the center of the spherical object.

Given:
Distance from the center of the spherical object, r = 7.3x[tex]10^8[/tex] m
Mass of the spherical object, M =[tex]3.0x10^27[/tex] kg

First, we need to calculate [tex]T^2[/tex]using the given values:

[tex]T^2 = (4π^2 / G * M) * r^3[/tex]

Plugging in the values:
[tex]T^2 = (4 * π^2 / (6.67430 × 10^-11 m^3 kg^-1 s^-2) * (3.0x10^27 kg)) * (7.3x10^8 m)^3[/tex]
Simplifying the equation:
[tex]T^2 = (4 * π^2 / (6.67430 × 10^-11 m^3 kg^-1 s^-2)) * (3.0x10^27 kg) * (7.3x10^8 m)^3[/tex]

Calculating [tex]T^2:[/tex]
[tex]T^2 = 1.75x10^20 s^2 * (3.0x10^27 kg) * (7.3x10^8 m)^3[/tex]
[tex]T^2 = 2.39x10^62 m^3 kg^-1 s^-2[/tex]

Now, we can find the orbital period T by taking the square root of[tex]T^2[/tex]:

[tex]T = sqrt(2.39x10^62 m^3 kg^-1 s^-2)[/tex]

Therefore, the orbital period for the object is approximately sqrt(2.39x10^62) seconds.

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