For astronomical objects, the time period can be calculated using:
T² = (4π²a³)/GM
where T is time in Earth years, a is distance in Astronomical units, M is solar mass (1 for the sun)
Thus,
T² = a³
a = ∛(29.46²)
a = 0.67 AU
1 AU = 1.496 × 10⁸ Km
0.67 * 1.496 × 10⁸ Km
= 1.43 × 10⁹ Km
Answer:
57.6Joules
Explanation:
Rotational kinetic energy of a body can be determined using the expression
Rotational kinetic energy = 1/2Iω²where;
I is the moment of inertia around axis of rotation. = 5kgm/s²
ω is the angular velocity = ?
Note that torque (T) = I¶ where;
¶ is the angular acceleration.
I is the moment of inertia
¶ = T/I
¶ = 3.0/5.0
¶ = 0.6rad/s²
Angular acceleration (¶) = ∆ω/∆t
∆ω = ¶∆t
ω = 0.6×8
ω = 4.8rad/s
Therefore, rotational kinetic energy = 1/2×5×4.8²
= 5×4.8×2.4
= 57.6Joules
Kepler's third law states that, for a planet orbiting around the Sun, the ratio between the cube of the radius of the orbit and the square of the orbital period is a constant:

(1)
where
r is the radius of the orbit
T is the period
G is the gravitational constant
M is the mass of the Sun
Let's convert the radius of the orbit (the distance between the Sun and Neptune) from AU to meters. We know that 1 AU corresponds to 150 million km, so

so the radius of the orbit is

And if we re-arrange the equation (1), we can find the orbital period of Neptune:

We can convert this value into years, to have a more meaningful number. To do that we must divide by 60 (number of seconds in 1 minute) by 60 (number of minutes in 1 hour) by 24 (number of hours in 1 day) by 365 (number of days in 1 year), and we get
An oven mitt is used to take the tray out of the oven because it’s an insulator.
Answer:
β2= β1+10*f
Explanation:
comparing β2 and β1, it is said that β2 is increased by a factor of f.
for each factor of f, there is a 10*f dB increase.
therefore if the β1 is increases by an intensity of factor f
the new intensity would be β1+ 10*f