Answer:
B. holding a coffee mug
Explanation:
Something must move a distance for work to be done.
Answer:
1.
Jupiter is the largest planet in the solar system. (Image credit: NASA)
The largest planet in the solar system, the gas giant Jupiter is approximately 318 times as massive as Earth. If the mass of all of the other planets in the solar system were combined into one "super planet," Jupiter would still be two and a half times as large.
2.Rotation of Jupiter
[/caption]
Jupiter has the fastest rotation of all the planets in the Solar System, completing one rotation on its axis every 9.9 hours.
3.Jupiter, the King of the Planets, is a gas giant, which means that it's made mostly of gases like hydrogen and helium, and that it doesn't have a solid surface in the way that rocky planets like Earth do. With a temperature of 130 K (-140 C, -230 F), it's so cold that it gives off most of its energy in the infrared. In fact, Jupiter gives off almost twice as much heat as it receives from the Sun. It's able to do this because it has its own internal heat source, powered by the slow gravitational collapse that started when the planet first formed. Astronomers estimate that Jupiter is currently shrinking by almost 2 cm per year
Answer:
a) K = 2/3 π G m ρ R₁³ / R₂
, b) U = - G m M / r
Explanation:
The law of universal gravitation is
F = G m M / r²
Part A
Let's use Newton's second law
F = m a
The acceleration is centripetal
a = v² / R₂
G m M / R₂² = m v² / R₂
v² = G M / R₂
They give us the density of the planet
ρ = M / V
V = 4/3 π R₁³
M = ρ V
M = ρ 4/3 π R₁³
v² = 4/3 π G ρ R₁³ / R₂
K = ½ m v²
K = ½ m (4/3 π G ρ R₁³ / R₂)
K = 2/3 π G m ρ R₁³ / R₂
Part B
Potential energy and strength are related
F = - dU / dr
∫ dU = - ∫ F. dr
The force was directed towards the center and the vector r outwards therefore there is an angle of 180º between the two cos 180 = -1
U- U₀ = G m M ∫ dr / r²
U - U₀ = G m M (- r⁻¹)
We evaluate for
U - U₀ = -G m M (1 / 
- 1 /
)
They indicate that for ri = ∞ U₀ = 0
U = - G m M / r
