Explanation

Kepler's Third Law of Planetary Motion states:

T² = (4π²/G * (M₁ + M₂)) * a³

Where:

T = Orbital Period

a = Semi-major Axis

G = Gravitational Constant

M₁ and M₂ = Masses of the two bodies (e.g., planet and star)

This law shows that the square of the orbital period (T) is proportional to the cube of the semi-major axis (a).

Explanation

Explanation

Explanation

Explanation

Explanation

To find the time it takes to decay 75% of the initial amount, we need to find the time it takes for 25% of the initial amount to remain.

Since the half-life is 4.5 × 10^9 years, after one half-life, 50% of the initial amount remains.

After two half-lives, 25% of the initial amount remains (50% of 50%).

Therefore, the time it takes to decay 75% of the initial amount is:

2 × half-life = 2 × 4.5 × 10^9 years = 9 × 10^9 years

Explanation

To find the increase in internal energy, we can use the equation:

ΔU = Q - W

where ΔU is the change in internal energy, Q is the heat energy added (which is the latent heat of vaporization in this case), and W is the work done.

Given:

Q = 2240 J (latent heat of vaporization of water per gram)

W = 168 J (work done in the process of vaporization)

Now, we can plug in the values:

ΔU = Q - W

= 2240 J - 168 J

= 2072 J

Explanation

Momentum (p) is proportional to velocity (v), while kinetic energy (KE) is proportional to v².

When momentum decreases by 20%, velocity decreases by 20%.

So, kinetic energy decreases by (1 - 0.8²) × 100% ≈ 36%.

Explanation

In a vacuum or free space, there are no particles or matter, so:

• Pressure (p) is zero.
• Current density (J) is also zero, since there are no charged particles to carry current.

Therefore, the correct observation is p = 0, J = 0.

Explanation