Jupiter2U School
Chapter 06

6. Gravity & Orbits

Middle School

Why does the Moon circle the Earth forever instead of flying off or crashing in? The answer is gravity, and the surprising idea of "falling around" a planet.

At a glance
Core ideaAn orbit is continuous free fall — moving sideways fast enough to keep missing the ground.
Key termOrbital speed — v = √(GM/r); farther orbits are slower.
You can…Compute how fast the ISS must travel to stay in orbit.
Watch outAstronauts float from free fall, not from an absence of gravity.
01 · Theory

Gravity pulls, but sideways motion saves you

Every object with mass pulls on every other object with mass — this is gravity. Newton described it precisely:

F = G m1m2 / r² G = 6.674×10⁻¹¹ N·m²·kg⁻²

An orbit happens when an object moves sideways fast enough that as gravity pulls it down, the ground curves away beneath it just as fast — so it keeps missing! Speed up enough, and you never hit the ground at all; you fall around the planet forever. Setting gravity equal to the centripetal force needed for a circular path gives the orbital speed:

v = √(GM / r)
02 · Explanation

Why astronauts float

Astronauts on the International Space Station are not "beyond gravity" — at their altitude, Earth's gravity is still about 90% as strong as on the ground. They float because they and their spacecraft are both continuously falling toward Earth together, at the same rate, while moving sideways fast enough to keep missing it. It's free fall, not an absence of gravity.

Key ideaA cannonball fired slowly falls to the ground. Fired faster, it lands farther away. Fired fast enough (about 7.9 km/s at Earth's surface), it falls all the way around the curve of the Earth and never lands — that's an orbit.
03 · Practical

Worked example — how fast does the ISS orbit?

The International Space Station orbits at about r = 6.79×10⁶ m from Earth's centre (roughly 420 km altitude). Earth's mass is M = 5.97×10²⁴ kg. Find its orbital speed.

Solution
  1. Use v = √(GM/r) with G = 6.674×10⁻¹¹.
  2. Compute the numerator: GM = 6.674×10⁻¹¹ × 5.97×10²⁴ = 3.98×10¹⁴.
  3. Divide by r: 3.98×10¹⁴ / 6.79×10⁶ = 5.87×10⁶.
  4. Take the square root: v = √(5.87×10⁶) ≈ 7 660 m/s — about 27,600 km/h.

Answer: roughly 7.7 km/s, fast enough to circle the entire Earth in about 90 minutes.

04 · Q&A

Test your understanding

Is there really no gravity in space near Earth?

False — a common myth. At the ISS's altitude, gravity is about 90% as strong as at Earth's surface. Astronauts feel weightless because they are in continuous free fall, not because gravity has switched off.

What would happen if the ISS suddenly stopped moving sideways?

It would simply fall straight down to Earth, pulled by gravity with nothing to counteract it. It's precisely the sideways speed that turns a fall into an endless orbit.

If you double the distance r between two masses, what happens to the gravitational force?

It drops to one quarter, since force depends on 1/r² — doubling r means dividing the force by 2² = 4.

Why do objects farther from Earth (like the Moon) orbit more slowly than the ISS?

Orbital speed is v = √(GM/r) — as r grows, v shrinks. Also, less gravitational pull is needed to keep a farther object curving around, so a slower sideways speed is enough. The Moon orbits at only about 1 km/s, compared to the ISS's 7.7 km/s.

Concept mind map

How the ideas connect

Every key idea in this chapter, branching from the core concept — use it to see the whole picture at a glance.

Gravity pulls downSideways speedContinuous freefallOrbit as fallingWeightlessnessISS orbitGravity and Orbits
Infographic

The key facts, visualised

~7.9 km/s
Orbital speed needed near Earth's surface (low orbit)
~90 min
Time the ISS takes to circle Earth once
~90%
Fraction of surface gravity still felt at ISS altitude
Solved examples

Worked problems, step by step

Follow each solution line by line, then try to reproduce it on paper before moving on.

Example 1The ISS orbits about every 90 minutes at roughly 400 km altitude, circling Earth (radius ~6,371 km). Estimate its speed.

  1. Orbit radius r = 6,371 + 400 = 6,771 km
  2. Circumference = 2 x pi x 6,771 = ~42,500 km
  3. Period T = 90 min = 5,400 s
  4. Speed = 42,500 km / 5,400 s = ~7.9 km/s

Example 2Why do astronauts float inside the ISS if gravity is still strong there?

  1. Gravity at that altitude is about 90% of surface value
  2. The station and astronauts fall together continuously
  3. Falling together means no support force, so they feel weightless
Practice problem set

Now you try

Work each one out first, then tap to reveal the worked answer.

1What keeps a satellite in orbit instead of falling straight down?
Its sideways (tangential) speed, which turns the fall into a curved orbit.
2Is there gravity at the ISS's altitude?
Yes, about 90% of surface gravity; astronauts float because they are in free fall.
3What would happen to a slow-moving object high above Earth with no sideways speed?
It would fall straight down toward Earth.
4Why do astronauts feel weightless?
They and the station fall together, so there is no support force on them.
5Roughly how fast must an object move to stay in low Earth orbit?
About 7.9 km/s.
6How long does the ISS take to circle Earth once?
About 90 minutes.