Orbital speed and gravity

Curriculum links

Quoted word for word from the official documents.

Step by step

The caption is what the class reads on screen; the talking points are in your notes drawer (N) when you present. Steps marked Pupils only appear only in the pupil lesson.

1. 01

   The inner planets race

   Presented and for pupils

   Caption

   Ten days pass every second here: Mercury goes round the Sun in under nine seconds, while Mars takes more than a minute.

   Talking points

   • NASA orbital periods: Mercury 88.0 days, Venus 224.7, Earth 365.2, Mars 687.0. At ten days a second that is 8.8 s, 22.5 s, 36.5 s and 68.7 s.
   • This view is at true scale, so the planets are far too small to see. The labels mark where they are.

   Sources 1 2Present from this step →

2. 02

   The giants crawl

   Presented and for pupils

   Caption

   Now a whole year passes every second, and even so Jupiter takes about 12 seconds to go round and Neptune almost three minutes.

   Talking points

   • NASA orbital periods: Jupiter 4,331 days (11.9 years), Saturn 10,747 days (29.4 years), Uranus 30,589 days (83.7 years), Neptune 59,800 days (163.7 years). The fact sheet notes give these from one vernal equinox to the next.
   • The camera is about 80 times as far from the Sun as Earth (farther on a narrow screen). True scale again: the labels mark the planets.

   Sources 1 2Present from this step →

3. 03

   Speed falls with distance

   Presented and for pupils

   Caption

   The farther a planet is from the Sun, the slower it travels along its orbit.

   Talking points

   • NASA average orbital speeds and distances from the Sun: Mercury 47.4 km/s at 57.9 million km, Venus 35.0 at 108.2, Earth 29.8 at 149.6, Mars 24.1 at 228.0, Jupiter 13.1 at 778.5, Saturn 9.7 at 1,432.0, Uranus 6.8 at 2,867.0, Neptune 5.4 at 4,515.0.
   • The fact sheet notes define the distance as the average distance from the Sun, the semi-major axis, and the speed as the average speed along the orbit.

   Ask the class

   Put these planets in order of orbital speed, fastest first.

   They start in this order: Jupiter, Mercury, Neptune, Earth.

   Answer

   1. Mercury
   2. Earth
   3. Jupiter
   4. Neptune

   WhyNASA's average orbital speeds: Mercury 47.4 km/s, Earth 29.8 km/s, Jupiter 13.1 km/s, Neptune 5.4 km/s. The closer to the Sun, the faster.

   Sources 1 2Present from this step →

4. 04

   Earth's speed

   Presented and for pupils

   Caption

   Earth's orbit is very nearly a circle, so its speed is the circumference, 2πr, divided by the time for one lap.

   Talking points

   • NASA: Earth's orbital eccentricity is 0.017, and its mean orbital speed 29.78 km/s, from 29.29 km/s at its slowest to 30.29 km/s at its fastest.
   • For Mercury, whose orbit is the most stretched of the planets (eccentricity 0.206), 2πr ÷ T gives 47.9 km/s, while NASA's average along the real ellipse is 47.4 km/s.

   Ask the class

   Earth orbits 149.6 million km from the Sun and takes 365.25 days to go round once. Find its orbital speed in km/s.

   Answer29.8 km/s. Answers from 29.6 to 30 are marked right.

   WhyDistance = 2π × 149,600,000 km = 939,960,000 km. Time = 365.25 × 24 × 3,600 = 31,557,600 s. Speed = 939,960,000 ÷ 31,557,600 = 29.8 km/s, NASA's figure.

   Sources 1 3 4 11Present from this step →

5. 05

   Gravity weakens with distance

   Presented and for pupils

   Caption

   The Sun's pull gets weaker with distance, so a planet farther out needs less speed to stay in orbit.

   Talking points

   • Edexcel 1AS0 8.9: the gravitational force between two bodies is proportional to the product of their masses and inversely proportional to the square of their separation.
   • NASA Earth Observatory says the same of satellites round Earth: closer in, the pull of gravity is stronger and the satellite moves more quickly.

   Ask the class

   If the distance between two bodies doubles, what happens to the gravitational force between them?

   1. AIt halves
   2. BIt falls to a quarterRight answer
   3. CIt doubles

   WhyThe force is inversely proportional to the square of the separation. Twice the distance gives 2² = 4 times less force, a quarter.

   Sources 9 12Present from this step →

6. 06

   Kepler's third law

   Presented and for pupils

   Caption

   Kepler's third law says T²/r³ is the same for every planet, and with T in years and r in astronomical units it comes to 1.

   Talking points

   • Check with NASA's values for Mars: 1.881 years and 1.524 au give 1.881² ÷ 1.524³ = 3.5382 ÷ 3.5396 = 0.9996.
   • NASA's Jupiter Fact Sheet gives a semi-major axis of 5.20336 au and a sidereal orbit period of 4,332.589 days, 11.862 years.
   • Edexcel 1AS0 8.7: the constant depends inversely on the mass of the central body, so satellites round Earth share a different constant from the planets.

   Ask the class

   Jupiter is 5.20 au from the Sun. Using T²/r³ = 1 (T in years, r in au), find how many years Jupiter takes to orbit the Sun.

   Answer11.9 years. Answers from 11.75 to 12.05 are marked right.

   WhyT² = 5.20³ = 140.6, so T = √140.6 = 11.86 years. NASA gives 11.862 years.

   Sources 5 6 12Present from this step →

7. 07

   Speed from Kepler

   Presented and for pupils

   Caption

   Put Kepler's law and speed = 2πr ÷ T together, and orbital speed falls as one over the square root of the distance.

   Talking points

   • Kepler: T is proportional to r^(3/2). Speed = 2πr ÷ T, so speed is proportional to r ÷ r^(3/2) = 1 ÷ √r.
   • NASA gives Neptune's mean distance as 4,515.0 million km, 30.2 times Earth's 149.6 million km, and its orbital speed as 5.4 km/s. With 30.2: 29.8 ÷ √30.2 = 5.42 km/s.

   Ask the class

   Neptune is about 30 times as far from the Sun as Earth. Orbital speed is proportional to 1/√r, and Earth moves at 29.8 km/s. Find Neptune's orbital speed in km/s.

   Answer5.4 km/s. Answers from 5.25 to 5.55 are marked right.

   WhySpeed = 29.8 ÷ √30 = 29.8 ÷ 5.48 = 5.44 km/s. NASA gives 5.4 km/s.

   Sources 1 7 12Present from this step →

8. 08

   Round Earth too

   Presented and for pupils

   Caption

   The same rule holds round Earth: the higher a satellite's orbit, the slower it moves.

   Talking points

   • NASA Earth Observatory: the higher a satellite's orbit, the slower it moves. ESA: low Earth orbit satellites travel at about 7.8 km/s and geostationary ones at about 3 km/s. NASA: the Moon, 384,400 km out, averages 1.022 km/s.
   • NASA Earth Observatory describes the paradox: to speed a satellite up, the operator fires the thrusters against its direction of motion, which drops it into a lower orbit where it moves faster.
   • This view of the Moon's orbit is not to scale.

   Ask the class

   A satellite operator wants a satellite to go round faster. What must happen to its orbit?

   1. AIt must move to a lower orbitRight answer
   2. BIt must move to a higher orbit
   3. CIt can stay at the same height and just speed up

   WhyFor a stable orbit the radius must change if the speed changes, and a faster orbit is a lower one. NASA notes the operator gets there by firing the thrusters against the direction of motion.

   Sources 8 9 10 11Present from this step →

9. 09

   Find the fastest planet

   Pupils only

   Caption

   Your turn: find the planet with the fastest orbit and click on it, or step to it with the arrows.

   Talking points

   • NASA: Mercury, closest to the Sun at 57.9 million km, has the fastest average orbital speed, 47.4 km/s.

   Pupil task

   Focus on the planet that moves fastest along its orbit.

   HintSpeed falls with distance from the Sun, so look closest in.

   The viewer checks the task as the pupil works and says when it is done.

   Sources 1Open this step as a pupil →

Sources

Every fact in this lesson comes from these sources, and each step lists the ones it uses.

1. Planetary Fact Sheet (metric), NASA NSSDCA
2. Notes on the Planetary Fact Sheets, NASA NSSDCA
3. Earth Fact Sheet, NASA NSSDCA
4. Mercury Fact Sheet, NASA NSSDCA
5. Mars Fact Sheet, NASA NSSDCA
6. Jupiter Fact Sheet, NASA NSSDCA
7. Neptune Fact Sheet, NASA NSSDCA
8. Moon Fact Sheet, NASA NSSDCA
9. Catalog of Earth Satellite Orbits, NASA Earth Observatory
10. Types of orbits, European Space Agency
11. AQA GCSE Physics (8463) specification, version 1.1
12. Pearson Edexcel GCSE (9-1) Astronomy (1AS0) specification, issue 3