Question

Uranus has moved 4.0 degrees across the sky in one year. Neptune has moved 2.1 degrees across the sky in one year.

1. How many degrees should a planet move across the sky when completing one revolution around the Sun? (Hint: It orbits in an ellipse, roughly the shape of a circle)

2. Calculate the orbital period of Uranus (in years), based on it moving 4.0 degrees in one year.

3. Calculate the orbital period of Neptune (in years), based on it moving 2.1 degrees in one year.

4. What is the theoretical (textbook) value for the orbital period of Uranus (in years)?

5. What is the theoretical (textbook) value for the orbital period of Neptune (in years)?

6. Compare your answers from questions 1 and 4. Calculate the percent error for the orbital period of Uranus.

7. Compare your answers from questions 2 and 5. Calculate the percent error for the orbital period of Neptune.

8. Using your results from question 2, use Kepler's third law, P²=a³, to calculate the average distance Uranus orbits the sun (in AU).

9. Using your results from question 2, use Kepler's third law, P²=a³, to calculate the average distance Neptune orbits the sun (in AU).

10. A planet called "Z" has been discovered 52.0 AU from the Sun. Using Kepler's 3rd Law, calculate the orbital period of the planet (in years).

11. Planet X moves 5 arc minutes in one year. What is the orbital period of Planet X (in years)? Remember that there are 60 arc minutes in one degree.

12. Find the gravitational force between Earth and the moon. The Moon's average distance from the Earth is 3.84 x 10⁸ meters. The Moon's mass is 7.34 x 10²² kg and the Earth's mass is 5.97 x 10²⁴. Use Newton's universal law of gravitation to solve for the force. The answer you get is going to be a large force in newtons. Enter ONLY the exponent of your answer below.

Answer 1

1. Assuming the shape f the orbit to be circle, the number of degrees the planet Uranus moved across the sky when completing one revolution around the Sun is .

2.

The angular distance moved by Uranus in one year

Thus the time taken by Uranus to complete one revolution () or the period

  

= 90 years

3.

The angular distance moved by Neptune in one year

Thus the time taken by Neptune to complete one revolution () or the period

  

= 171.43 years

4.

The theoretical (textbook) value for the orbital period of Uranus (in years) = 84

5.

The theoretical (textbook) value for the orbital period of Neptune (in years) = 165

6.

Formula for percentage error

where

Calculated period

Observed period

The percent error for the orbital period of Uranus =

7.

The percent error for the orbital period of Neptune =

8.

We have Kepler's third law

Using this equation, the average distance of Uranus from the sun (in AU)

  

  

9.

The average distance of Neptune from the sun (in AU)

  

  

  

10.

The distance of planet "Z" from the Sun,

Then the orbital period of the planet in days

  

  

  

Then the orbital period of the planet in years

   years

11.

Angular distance moved by the planet X = 5 minutes of arc

  

Then the orbital period of Planet X

  

   years

12.

Moon's average distance from the Earth,

Moon's mass,

Earth's mass is

The gravitational force between Earth and the moon,

where