Answer:
5.024 years
Explanation:
T1 = 1 year
r1 = 150 million km
r2 = 440 million km
let the period of asteroid orbit is T2.
Use Kepler's third law
T² ∝ r³
So,


T2 = 5.024 years
Thus, the period of the asteroid's orbit is 5.024 years.
Answer: 
Explanation:
We are told both planets describe a circular orbit around the star S. So, let's approach this problem begining with the angular velocity
of the planet P1 with a period
:
(1)
Where:
is the velocity of planet P1
is the radius of the orbit of planet P1
Finding
:
(2)
(3)
(4)
On the other hand, we know the gravitational force
between the star S with mass
and the planet P1 with mass
is:
(5)
Where
is the Gravitational Constant and its value is 
In addition, the centripetal force
exerted on the planet is:
(6)
Assuming this system is in equilibrium:
(7)
Substituting (5) and (6) in (7):
(8)
Finding
:
(9)
(10)
Finally:
(11) This is the mass of the star S
The graph of the potential energy pass through zero origin, cuts across positive x-axis and negative x-axis.
<h3>Slope of the graph</h3>
The slope of the graph when the potential energy of a particle constrained in on x-axis is determined as follows;
F = -dU/dx
-dU = Fdx
dU = -Fdx
U = -∫(kx + ax³)dx
U = kx²/2 - ax⁴/4
When, x = 0, U = 0
When U = 0;

The graph of the potential energy pass through zero origin, cuts across positive x-axis and negative x-axis.
Complete question is below:
Suppose that the potential energy of a particle constrainedon x-axis and subjected to a force in the same direction, at a fuction of F(x) = -kx + ax³.
Find the functional form of the potential energy.
Learn more about potential energy here: brainly.com/question/1242059
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Answer:
4Al + 3O2 + heat ------> 2Al2O3
Explanation:
It is endothermic reaction.