Скачать или смотреть How Satellite Energy & Orbital Speed Change with Altitude

In this physics lesson, we cover energy of satellites orbiting Earth. Learn how to calculate kinetic, potential, and total mechanical energy in orbital motion and why astronauts feel weightless in space
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What You’ll Learn

1. Calculate the gravitational potential energy of a satellite using U = –GMm / r
2. Derive the kinetic energy of a satellite in circular orbit as K = GMm / 2r
3. Understand why total mechanical energy E = –GMm / 2r stays constant in orbit
4. Use the orbital velocity formula v = √(GM / r) to link speed and altitude
5. Explain why orbital speed doesn't depend on satellite mass
6. Apply Kepler’s Third Law to find the orbital period: T = 2π√(r³ / GM)

Key Concepts Covered
satellite orbits, gravitational potential energy, kinetic energy of a satellite, total mechanical energy, orbital velocity, orbital period, circular orbits, Kepler’s Third Law

Why This Lesson is Important
Understanding how energy behaves in satellite motion is key for mastering orbital mechanics in AP Physics, JEE, NEET and IB exams. These principles also explain real-world phenomena like why satellites don’t fall and why astronauts feel weightless in orbit—making this both an important exam topic and an introduction to space science.

Prerequisite or Follow-Up Lessons

Prerequisite: Newton’s Law of Universal Gravitation
Follow-Up: Kepler’s Laws of Planetary Motion – Explained with Derivations

Full Lesson Transcript – Satellite Energy and Orbital Motion

Changing Energy in Orbit
A satellite orbiting Earth in an elliptical path has a varying speed, which changes its kinetic energy. At the same time, its distance from Earth’s center changes, so its gravitational potential energy also fluctuates. But one thing remains constant: the total mechanical energy of the satellite.

Since the satellite’s mass is negligible compared to Earth’s, we assign the total energy of the Earth-satellite system to the satellite itself.

Gravitational Potential Energy
The potential energy of a satellite is given by:
U = –GMm / r

Kinetic Energy in Circular Orbit
½mv² = GMm / 2r
So the kinetic energy K = GMm / 2r.
Since the potential energy is U = –GMm / r, we see that:
K = –U / 2

Orbital Speed Formula
From the same relationship, we can find orbital speed:
v = √(GM / r)
This means once you fix r (the orbital radius), the speed v is automatically determined. You cannot choose both independently.

Another key insight: satellite mass m doesn’t appear in the orbital speed formula. That means a 100 kg satellite and a 500 kg satellite at the same height will move at the same speed.

Why Astronauts Float in Orbit
This also explains weightlessness. Astronauts float inside a shuttle because both are in freefall around Earth at the same speed. Since there's no normal force between them and the shuttle, they experience apparent weightlessness.

Finding the Orbital Period
The time period T of the orbit can be found using:
v = 2πr / T or
√(GM / r) = 2πr / T gives
T = 2π × √(r³ / GM)

This is a special case of Kepler’s Third Law, which says that the square of the period is proportional to the cube of the radius.

Total Mechanical Energy
Total energy E is the sum of kinetic and potential energy:
E = K + U = (GMm / 2r) – (GMm / r)
E = –GMm / 2r

So total energy is negative and equal to –K.

Elliptical Orbits and Semimajor Axis
For elliptical orbits, replace r with the semimajor axis a:
E = –GMm / 2a

The total energy depends only on the semimajor axis, not on the orbit’s eccentricity. So all orbits with the same a will have the same total energy.

Energy Trends with Orbit Radius
As orbital radius r increases:
Kinetic energy decreases
Orbital speed decreases
Potential energy becomes less negative
Total energy becomes less negative

At very large distances (r → ∞), all energy values approach zero. That’s why satellites in low Earth orbit have higher speeds and more negative energy than those in geosynchronous orbit.

Key Moments:
0:00 – Gravitational Potential Energy
0:38 – Kinetic Energy in Orbit
1:27 – Kinetic-Potential Energy Relation
2:00 – Speed Depends on Orbit, Not Mass
3:10 – Why Astronauts Float
3:42 – Time Period and Kepler’s Law
4:35 – Total Mechanical Energy

Who is this for: Class 11 physics students, AP Physics students, students appearing for competitive exams like IIT JEE and NEET.
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