Worksheet: Mechanical Energy Conservation in Orbits

In this worksheet, we will practice calculating the kinetic energy required to maintain circular orbit around a star or planet.

Q1:

The figure shows a planet orbiting a star along an elliptical path.

At which of the labeled points on the figure would the gravitational potential energy of the planet have the highest value?

  • APoint C
  • BPoint D
  • CPoint E
  • DPoint B
  • EPoint A

At which of the labeled points on the figure would the kinetic energy of the planet be greatest?

  • APoint C
  • BPoint D
  • CPoint B
  • DPoint E
  • EPoint A

As the planet moves from point D to point C, does its gravitational potential energy increase, decrease, or stay the same?

  • AIt stays the same.
  • BIt decreases.
  • CIt increases.

As the planet moves from point C to point B, does its kinetic energy increase, decrease, or stay the same?

  • AIt stays the same.
  • BIt increases.
  • CIt decreases.

Q2:

The diagram shows two planets orbiting a star. Both planets have the same mass. Planet 2 orbits the star at a radius twice that of planet 1.

What is the ratio of the kinetic energy of planet 2 to that of planet 1?

  • A4
  • B 1 4
  • C 1 2
  • D1
  • E2

Q3:

Which of the five lines on the graph correctly shows how the kinetic energy of an object in a circular orbit varies with the radius of the orbit?

  • AThe green line
  • BThe purple line
  • CThe blue line
  • DThe red line
  • EThe black line

Q4:

The diagram shows two planets orbiting a star. Both planets have the same kinetic energy. Planet 2 orbits the star at a radius three times that of planet 1.

What is the ratio of the mass of planet 2 to that of planet 1?

Q5:

At a distance 𝑅 away from a planet, an object with a mass 𝑀 has a gravitational potential energy of 4.00 GJ. Its velocity is tangential to the line connecting the center of mass of the object and the planet.

If the object has a kinetic energy of 2.00 GJ, what will happen to it?

  • AIt will completely escape the planet’s gravitational pull.
  • BIt will orbit the planet along a circular path.
  • CIt will move closer to the planet, gaining kinetic energy. Its increased kinetic energy will cause it to move further away from the planet again, and the object will follow an elliptical orbit.
  • DIt will move further away from the planet before being pulled back toward it by gravity, following an elliptical orbit.

If the object has a kinetic energy of 3.00 GJ, what will happen to it?

  • AIt will orbit the planet along a circular path.
  • BIt will move further away from the planet before being pulled back toward it by gravity, following an elliptical orbit.
  • CIt will move closer to the planet, gaining kinetic energy. Its increased kinetic energy will cause it to move further away from the planet again, and the object will follow an elliptical orbit.
  • DIt will completely escape the planet’s gravitational pull.

Q6:

Which of the following formulas gives the ratio of the kinetic energy, 𝐸 K , to the gravitational potential energy, 𝐸 P , of an object that is in a circular orbit?

  • A 𝐸 = βˆ’ 𝐸 2 K P
  • B 𝐸 = βˆ’ 𝐸 K P 
  • C 𝐸 = βˆ’ 4 𝐸 K P
  • D 𝐸 = βˆ’ 2 𝐸 K P
  • E 𝐸 = βˆ’ 𝐸 4 K P

Q7:

The 2001 Mars Odyssey is a spacecraft orbiting Mars. The radius of its orbit is 3,790 km, and it has a mass of 376 kg. What is the kinetic energy of the spacecraft? Use a value of 6 . 4 2 Γ— 1 0   kg for the mass of Mars and 6 . 6 7 Γ— 1 0    m3/kgβ‹…s2 for the universal gravitational constant. Give your answer to 3 significant figures.

Q8:

Which of the following formulas correctly describes the relation between the kinetic energy of an object in a circular orbit and the radius of the orbit?

  • A 𝐸 ∝ √ π‘Ÿ οŒͺ
  • B 𝐸 ∝ 1 π‘Ÿ οŒͺ 
  • C 𝐸 ∝ 1 π‘Ÿ οŒͺ
  • D 𝐸 ∝ π‘Ÿ οŒͺ 
  • E 𝐸 ∝ π‘Ÿ οŒͺ

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