About Kepler's Law

Kepler's Law: The Mathematical Formula for Planetary Motion

In 1609, Johannes Kepler published his first two laws of planetary motion, which laid the mathematical foundation for our understanding of how planets move in space. Kepler's First Law states that planets move in elliptical orbits with the sun at one focus. Kepler's Second Law states that a planet's orbital speed is directly proportional to its distance from the sun. These laws are still used today to calculate the paths of spacecraft and predict eclipses. In this post, we will explore Kepler's Laws in more detail and see how they can be applied to real-world situations!

Kepler's First Law: The orbit of a planet is an ellipse with the sun at one of the foci.

An ellipse is a closed curve where the sum of the distances from any point on the curve to both foci is constant. This means that, as a planet moves around its orbit, it will sometimes be closer to the sun (perihelion) and sometimes be further away (aphelion). Kepler's First Law can be used to calculate the size of a planet's orbit. For example, if we know the distance from the sun to the planet at perihelion and aphelion, we can use Kepler's First Law to calculate the size of the orbit!

Kepler's Second Law: A planet's orbital speed is directly proportional to its distance from the sun.

This law states that a planet moves faster when it is closer to the sun and slower when it is further away. Kepler's Second Law can be used to calculate a planet's orbital period (the time it takes to complete one orbit). For example, if we know the distance from the sun to a planet at perihelion and aphelion, we can use Kepler's Second Law to calculate the orbital period!

Following are some of the multiple choice questions on the Kepler's Law with answers that will help the students in developing their knowledge.

Kepler's Law MCQ

1. What is inertia?

  • amount of atoms
  • amount of gravitational pull
  • the size
  • resistance to a change in motion

2. A year on Jupiter is 4,344 days long. This tells you how long it takes

  • Jupiter to rotate one time on its axis.
  • Earth to orbit Jupiter.
  • Jupiter to orbit the sun
  • the sun to orbit Jupiter

3. Who was Kepler?

  • Scientist
  • German Astronomer and mathematician

4. The period of geostationary artificial satellite is

  • 6 hours
  • 12 hours
  • 24 hours
  • 48 hours

5. Earth's spinning on its axis is called its _____________.

  • orbit
  • rotation

6. The study of space

  • Astronomy
  • Meteorology
  • Galaxy
  • Geology

7. Kepler’s third law states

  • The semimajor axis is equal to the planet’s average distance from the sun
  • None of these answers is correct
  • The square of the orbital period of a planet is proportional to its orbital radius
  • The orbit of a planet around the sun is an ellipse, with the sun at one focus

8. When the earth is closest to the sun

  • the sun will have the biggest apparent diameter and the greatest gravitational attraction
  • the sun will have the biggest apparent diameter and the smallest gravitational attraction

9. What is obliquity?

  • The measure of the tilt of the Earth
  • The change in the shape of Earth’s orbit around the sun
  • The change in the orientation of Earth’s axis
  • The measure of solar intensity of the sun

10. When a planet orbits the Sun, one of the foci of the elliptical orbit is

  • the axis
  • the perihelion
  • the center
  • the Sun

11. Planets revolve around the sun in elliptical orbits

  • Law of Periods
  • Law of orbits
  • Law of Areas
  • None of these

12. How fast does the earth revolve around the sun?

  • 15 degrees per hour
  • 1 degree per hour
  • 1 degree per day
  • 15 degrees per day

13. What is Kepler's 3rd Law?

  • Law of Areas
  • Law of Periods
  • Law of Orbits
  • None of these

14. What is his nationality

  • Chinese
  • Turkish
  • German
  • Russian

15. Which planet has the least eccentric orbit?

  • Venus
  • Mars
  • Mercury
  • Earth

16. What is Kepler's 2nd Law?

  • Law of Orbits
  • Law of Periods
  • Law of Areas
  • None of these

17. What is Kepler's 1st Law?

  • Law of Orbits
  • Law of Periods
  • Law of Areas
  • All of above

18. What causes Earth’s year to be shorter than Jupiter’s year?

  • the shape of Earth’s orbit around the Sun
  • the mass and density of Jupiter
  • the distance between Earth and the Sun
  • What causes Earth’s year to be shorter than Jupiter’s year?

19. Double the product of the masses of two objects

  • 4 times weaker gravity force
  • 2 times weaker gravity force
  • 4 times stronger gravity force
  • 2 times stronger gravity force

20. What unit to we usually use to to measure a planet's orbital period?

  • year
  • astronomical unit

21. What will result in the most eccentric elliptical orbit

  • when the focal points are on top of one another
  • then the focal points are farthest apart
  • when the focal points are closest together
  • All of above

22. What is it called when earth reaches the point in orbit when it is farthest from the sun?

  • Perihelion
  • Aphelion

23. Which model of the solar system can explain all observations

  • geocentric model
  • heliocentric model

24. What is the name of the backward motion of planets that cannot be explained by the geocentric model?

  • retrograde motion
  • revolutionary motion

25. Unit of 'G' is

  • N-m2/kg
  • N-m/kg2
  • N-m2/kg2
  • N-m/kg

26. 'G' is called

  • acceleration due to gravity
  • gravity
  • gravitational constant
  • gravitational force

27. When the distance between two objects increases the gravitational force between them

  • decreases
  • increases
  • no change
  • None of these

28. When the mass of the objects increases the gravitational force between them

  • decreases
  • increases
  • no change
  • Both A & B

29. Who proposed Earth centered model?

  • Ptolemy
  • Copernicus
  • Kepler
  • Tycho Brahe

30. Types of celestial coordinate system

  • Latitude and longitude
  • Ecuatorial and horizontal
  • None
  • All of above

31. What family is he from?

  • His parents was poor
  • He didn't have a family

32. What is the second law of Kepler ?

  • All planets move around the Sun in elliptical orbits, with the Sun as one focus of the ellipse.
  • The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
  • The radius vector of a planet sweeps over in equal areas in equal intervals of time.
  • None of these

33. What is the third law of Kepler

  • The square of the period of any planet is proportional to the cube of the semimajor axis of its orbit.
  • None

34. What is the line connecting the sun and planet

  • Line
  • Area
  • Imagine
  • Radius vector

35. Firs law of Kepler?

  • None
  • The orbit of planet is an ellipse with the Sun at one of the two foci
  • The radius vector of a planet sweeps over equal areas in equal time intervals of time.
  • The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit

36. The accelerations due to gravity on the surfaces of two planets are equal in magnitudes if

  • mass
  • \frac{mass}{radius^3} radius 3 mass ​
  • radius 2 mass ​
  • none of the above

37. If r represents the radius of the orbit of a satellite of mass m moving round a planet of mass M the velocity of the satellite is given by

  • v2 = GMmrv^2\ =\ \frac{GMm}{r}v2 = rGMm​
  • v2 = gMRv^2\ =\ \frac{gM}{R}v2 = RgM​
  • v=\frac{GMm}{r^2} v= r 2 GMm ​
  • V= ( r GM ​ ) ​

38. What is the reason for the motion of the moon on its orbit?

  • The gravitational force exerted by the sun
  • The gravitational force exerted on the Moon by the earth

39. What is the correct formula to calculate eccentricity?

  • Focal distance / major axis length
  • major axis length / minor axis length
  • minor axis length / major axis length
  • All of above

40. The factors that can determine the force between two objects include all of the following except

  • distance between the 2 objects
  • diameter of the objects

41. Where are the focal points located in a perfect circle?

  • close together
  • on top of each other

42. Earth will travel fastest in its orbit when

  • the earth is closest to the sun (January 3rd)
  • The earth is closest to the sun (July 3rd)

43. Which statement correctly describes when the earth is closest to the sun

  • It is called perihelion and it occurs on July 3rd
  • It is called aphelion and it occurs on July 3rd
  • It is called perihelion and it occurs on January 3rd
  • None of these

44. The planet with the most eccentric orbit is

  • Venus
  • Mars
  • Earth
  • Mercury

45. What effect does increasing the distance between an ellipse’s foci have on the shape of an ellipse?

  • Increases eccentricity
  • no effect

46. How can the position of the sun in earth's orbit be described?

  • The sun is at one of the two focal points of a slightly eccentric ellipse
  • The sun is at one of the two focal points of a highly eccentric ellipse

47. Where will an object move at the greatest speed as it orbits the sun?

  • Aphelion
  • Between perihelion and aphelion
  • Perihelion
  • None of these

48. What did Kepler discover about planets and their orbital speed?

  • Planets with the greatest mass will orbit the Sun with the fastest orbital speed.
  • Planets furthest from the Sun will orbit with the fastest orbital speed.
  • Planets closest to the Sun will orbit with the fastest orbital speed.
  • Planets with the least mass will orbit the Sun with the fastest orbital speed.

49. Double the distance between two objects

  • 4 times greater gravity attraction
  • 2 times weaker gravity
  • 4 times weaker gravity attraction
  • 2 times greater gravity

50. Which of the following can decrease the gravity between objects?

  • Remove mass
  • Decrease distance

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