Explanation:
We have,
Semimajor axis is 
It is required to find the orbital period of a dwarf planet. Let T is time period. The relation between the time period and the semi major axis is given by Kepler's third law. Its mathematical form is given by :

G is universal gravitational constant
M is solar mass
Plugging all the values,

Since,

So, the orbital period of a dwarf planet is 138.52 years.
Answer:

Given:
Mass of the polar bear (m) = 6.8 kg
Speed of the polar bear (v) = 5.0 m/s
To Find:
Kinetic energy of the polar bear (KE)
Explanation:
Formula:

Substituting values of m & v in the equation:





Kinetic energy of the polar bear (KE) = 23002.1 J
Answer:

Explanation:
The rotated angle is given by:

Since this is a quadratic equation it can be solved using:

Rewriting our equation:


Since
we discard the negative solution.

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