A planet orbits its star in a circular orbit (uniform circular motion) of radius 1.62x10^11 m. The orbital period of the planet around its star is 37.0 years. Determine the following quantities for this orbital motion: Angular acceleration , Tangential acceleration, Radial acceleration, Angular velocity, and Tangential velocity
See your 11-13 11,9:06pm post for solution.
To determine the quantities for this orbital motion, we'll use the following formulas:
1. Angular acceleration (α): α = (2π) / T
2. Tangential acceleration (at): at = r * α
3. Radial acceleration (ar): ar = (v²) / r
4. Angular velocity (ω): ω = (2π) / T
5. Tangential velocity (vt): vt = r * ω
where:
- T is the orbital period of the planet around its star,
- r is the radius of the circular orbit,
- α is the angular acceleration,
- at is the tangential acceleration,
- ar is the radial acceleration,
- ω is the angular velocity, and
- vt is the tangential velocity.
Given:
- Radius of the circular orbit (r) = 1.62x10^11 m
- Orbital period (T) = 37.0 years = 37.0 * 365 * 24 * 60 * 60 seconds
Let's calculate each quantity step by step:
1. Angular acceleration (α):
Using the formula: α = (2π) / T
Substitute the given value of T: α = (2π) / (37.0 * 365 * 24 * 60 * 60 seconds)
Calculate to get the answer in radians per second squared.
2. Tangential acceleration (at):
Using the formula: at = r * α
Substitute the known values of r and α: at = (1.62x10^11 m) * α
Calculate to get the answer in meters per second squared.
3. Radial acceleration (ar):
Using the formula: ar = (v²) / r
Since we don't have the velocity (v) yet, we'll calculate it later.
4. Angular velocity (ω):
Using the formula: ω = (2π) / T
Substitute the given value of T: ω = (2π) / (37.0 * 365 * 24 * 60 * 60 seconds)
Calculate to get the angular velocity in radians per second.
5. Tangential velocity (vt):
Using the formula: vt = r * ω
Substitute the known values of r and ω: vt = (1.62x10^11 m) * ω
Calculate to get the tangential velocity in meters per second.
After calculating these quantities, you will have determined the angular acceleration, tangential acceleration, radial acceleration, angular velocity, and tangential velocity for the given orbital motion.