Category: 07 Gravitation

# Space Travel

The Falcon has landed!!!

SpaceX launch webcasts are very exciting to watch, especially if you know a little of gravitation.

Lift off 22:56 | Meco 25:25 | Falcon Landing 32:20 | Deploy 1 37:25 | Deploy 2 38:35 | Deploy 3 39:15 | Deploy 4 40:23 | Deploy 5 41:05 | Deploy 6 41:58

In the old days, NASA used to fly the space shuttle.

# Apparent Weightlessness

In an orbiting space station, where the gravitational acceleration is exactly equal to the centripetal acceleration, apparent g drops to zero.

Actually, it does not have to be centripetal acceleration. As long as we free fall together with our (also free falling) vehicle, we become weightless.

As long as the plane accelerates at g downward, you experience zero g.

# How Earth’s Rotation affects g

The Earth’s rotation actually causes us to “lose weight” at the equator.

The Earth’s rotation also causes the acceleration of free fall to be lower at the equator.

So how big an effect does the Earth’s rotation have?

# Polar Orbit

Is it possible for one satellite to pass over every corner of the Earth?

Firstly, the satellite’s orbit muts have a high inclination of close to 90°. Only then will it be able to pass over the polar regions. Secondly, the altitude must be low so that it has a high resolution view of the Earth surface. By “raster scanning” the Earth, the entire Earth’s surface can be mapped out after multiple passes.

Many photographers love night scene photography. The ultimate night scene photo is probably that of the Earth from above the atmosphere, shown in the video below. The complete picture is constructed from the images acquired by the Suomi National Polar-orbiting Partnership Satellite (Suomi NPP). It took 312 satellite orbits to get a clear shot of every parcel of land surface.

# Geostationary Orbit

What does the view from the Electro-L, a geostationary satellite look like? Check out this video!

Well, the Earth looks like it has stopped rotating. That’s because we are on a geostationary satellite! The satellite is orbiting in the equatorial plane at the same angular velocity as the rotational speed of the earth. So the Earth looks stationary from the satellite, and the satellite looks stationary from the Earth.

Geostationary orbits are perfect for communication and broadcast satellites. Because a GEO satellite remain at the same spot in the sky, ground antennas do not have to track its movement across the sky, but instead just point permanently at its position in the sky.

A geostationary orbit can only be attained at an altitude of close to 36,000 km. From such high altitude, it takes only 3 GEO satellites to provide coverage for the majority of the Earth surface.

However, the polar regions will always be out of reach from the GSO. Since the GEO satellites orbit in the equatorial plane, they are always below the horizon at lattitudes above about 81°.

Being so far from Earth, the time taken for a signal to travel between Earth and the satellite is a few hundred ms. This poses problems for latency-sensitive applications such as live voice calls.

(sources: images from http://www.rap.ucar.edu/~djohnson/satellite/coverage.html)

# Global Positioning System

The Global Positioning System (GPS) consists of a constellation of (currently about 32) satellites. Orbiting at an altitude of 20,000 km, GPS satellites have orbital period of 12 hours.

So how does GPS work?

Firstly, every GPS satellite continuously broadcast its current time and position. What a GPS receiver must do, is to monitor the time and position information of the GPS satellites in its sight, and use those information to calculate its position on Earth. At a minimum, four satellites must be in view of the receiver for it to compute four unknown quantities (three position coordinates and clock deviation from satellite time).

So these satellites are really like landmarks (or “skymarks”) planted in the sky. Just that to keep them from falling back to Earth, we have to arrange them to keep circling the Earth. 🙂

# International Space Station

This video shows the view of the Earth from the International Space Station (ISS).

The ISS orbits at about 400 km above the Earth’s surface, making it a gigantic LEO satellite. Falling at 7.66 km/s, it views the sunrise/sunset every 90 minutes or so.

(source: wikipedia)

The ISS orbits at an inclination of 51.6°. This means the ISS does not pass over regions which lie above 51.6° N and 51.6 S° latittudes.

(source: NASA tumblr)
(The altitude is greatly exaggerated in the above animation)

Because the earth rotates “underneath” the ISS, the ISS advances in longitude after each orbit. This allows the ISS to pass over different regions of the earth during each orbit.