Multiple Choice
A comet is in a highly elliptical orbit around the Sun with a period of 2400 years. If this comet has a mass of approximately kg, what is the total energy of its orbit?
8. Centripetal Forces & Gravitation
Energy of Elliptical Orbits
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Pluto travels in a fairly elliptical orbit around the Sun. At its closest distance of km, its orbital speed is 6.12 km/s. At its farthest, its orbital speed reduces to just 3.71 km/s. How far is it from the Sun at this point (in km)?
A
km
B
km
C
km
D
km
Verified step by step guidance1
Recognize that this problem involves the conservation of angular momentum, which states that the angular momentum of Pluto at its closest point to the Sun (perihelion) is equal to its angular momentum at its farthest point (aphelion).
The formula for angular momentum (L) is given by L = m * v * r, where m is the mass of Pluto, v is its velocity, and r is the distance from the Sun. Since the mass of Pluto (m) remains constant, it can be canceled out from the equation.
Set up the equation for conservation of angular momentum: v1 * r1 = v2 * r2, where v1 and r1 are the velocity and distance at perihelion, and v2 and r2 are the velocity and distance at aphelion.
Substitute the known values into the equation: (6.12 km/s) * (4.43 × 10^9 km) = (3.71 km/s) * r2.
Solve for r2 by dividing both sides of the equation by 3.71 km/s to find the distance from the Sun at Pluto's farthest point.
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