Gravitation Concept Page - 10

Definition

Geostationary Satellite

A geostationary satellite is an earth-orbiting satellite, placed at an altitude of approximately 35,800 kilometers (22,300 miles) directly over the equator, that revolves in the same direction the earth rotates (west to east).

Application: Geostationary satellites appear to be fixed over one spot above the equator.Receiving and transmitting antennas on the earth do not need to track such a satellite. These antennas can be fixed in place and are much less expensive than tracking antennas. These satellites have revolutionized global communications, television broadcasting and weather forecasting, and have a number of important defense and intelligence applications.

Example

Orbital speed and distance from earth's surface of geostationary satellite

Example: A satellite can be in a geostationary orbit around earth at a distance r$r$ from the centre. If the angular velocity of earth about its axis doubles, a satellite can now be in a geostationary orbit around earth if its distance from the centre is related by following what relation?

Solution:  for a geostationary satellite, angular velocity of satellite is same as that of earth i.e. ωs=ωe${\omega }_s={\omega }_e$
initial
ωs=GMr3−−−−√${\omega }_s=\sqrt{{\displaystyle \frac{GM}{r^3}}}$. if earth's angular velocity is
doubled, lets change the radius to R$R$ to make it geostationary.
So, final ωs=GMR3−−−−√=2GMr3−−−−√${\omega }_s=\sqrt{{\displaystyle \frac{GM}{R^3}}}=2\sqrt{{\displaystyle \frac{GM}{r^3}}}$
solving this we get, R=r4(13)$R={\displaystyle \frac{r}{4^{\left({\displaystyle \frac{1}{3}}\right)}}}$

Definition

Polar Satellite

NASA science spacecraft designed The Global Geospace Science (GGS) Polar Satellite to study the polar magnetosphere and aurora Sensors on the spacecraft. Technically, which gathered multi-wavelength imaging of the aurora, and measured the entry of plasma into the polar magnetosphere and the geomagnetic tail, to study the flow of plasma to and from the ionosphere, and the deposition of particle energy in the ionosphere and upper atmosphere.

Data from the Polar satellites support a broad range of environmental monitoring applications including forecasting, weather analysis, climate research and prediction, global sea surface temperature measurements, atmospheric soundings of temperature and humidity, ocean dynamics research, volcanic eruption monitoring, forest fire detection, global vegetation analysis, search and rescue, and applications in many other fields.

Definition

Time period of polar satellites

Polar satellites are low altitude satellites at the height of 500-800 km, revolving around the poles of the earth in north-south direction. Its time-period is about 100 minutes.

Definition

Application of satellites

• Satellites can be used to get information about astronomical events.
• Satellites helps in weather forecasting.
• It helps in television and radio communication.
• It helps to find locations during combat situations.
• It helps in surveillance purposes by military.

Example

Weather monitoring satellite

Weather satellites carry instruments called radiometers that scan the Earth to form images. These instruments have small telescope or antenna, a scanning mechanism, and one or more detectors. That detect visible, infrared, microwave radiation for the purpose of monitoring weather systems around the world. Most of the satellites and instruments they have are designed to operate for 3 to 7 years, although many of them last much longer than that.

Advantages of geostationary satellite:
Orbit with the satellite at a very high altitude (about 22,500 miles) and orbiting over the equator at the same rate that the Earth turns. This allows the satellite to view the same geographic area continuously and is used to provide most of the satellite imagery you see on TV or the internet.

The disadvantages of a geostationary satellite:
The orbit is at very high altitude, which requires elaborate telescopes and precise scanning mechanisms in order to image the Earth at high resolution; and only a portion of the Earth can be viewed.

Definition

Describe the possible cases of projection of satellite

The different cases of projection of satellites are as follows:

• Circular  : if v=vc$v=v_c$
• Elliptical  : If ve>v>vc$v_e>v>v_c$
• Parabolic  : if v=ve$v=v_e$
• Hyperbolic : if v>ve

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