# Calculating the Acceleration of Spacecraft Orbiting Earth

Since 1957 when the first artificial satellite was launched, thousands of spacecraft have orbited Earth. While some are placed into polar orbits for communications or weather purposes, others such as communications satellites orbit in geostationary orbits for longer-term performance.

Like throwing a ball into the air creates an unpredictable path towards its landing point, spacecraft are also designed to navigate Earth in an orderly manner by striking an equilibrium between forward momentum and gravitational pull.

## Orbits

Spacecraft are capable of staying in orbit by matching their velocity with Earth’s gravitational pull, and by expending enough energy to combat it. As speed increases, more energy must be expended to counter this force; most satellites usually only need fuel for two purposes: altering orbit or avoiding debris collisions.

A satellite’s orbit depends on several factors, including its height, eccentricity and inclination relative to Earth’s equatorial plane; as well as what view of our planet it offers.

Sun-synchronous (sun-SIN-kron-ous) satellites, which orbit at approximately the same time every day, are known as sun-synchronous satellites (sun-SIN-kron-ous). Their unique polar orbit enables them to observe Earth from all corners without being obscured by atmospheric obscurity; such orbits are popularly used for navigation satellites and remote sensing purposes. At present there are 56 geosynchronous orbit satellites primarily utilized for communications, satellite radio and remote sensing activities.

## Distances

Distance from Earth for any spacecraft depends on its orbit and can be affected by factors like its shape and size as well as initial speed from launch affecting final velocity and distance from planet.

Satellites in lower-Earth orbit (LEO) orbit closer to Earth than their higher counterparts and are frequently utilized for satellite imaging due to higher resolution capabilities. Furthermore, LEO orbit serves as home for the International Space Station where astronauts spend months at a time living and working aboard its facilities.

Middle orbit satellites (GEO and MEO) cover more of Earth as they pass over both poles. Their elliptical orbits allow them to track changes on the ground as Earth rotates, such as weather patterns.

Spacecraft traveling at extreme velocities are typically far removed from Earth, due to velocities exceeding its gravitational force. Still, they must know where they are in space using “dead reckoning,” which measures the round trip time it takes for radio signals from their spacecraft back to Earth and back again.

## Velocity

Each orbit a satellite undertakes requires it to maintain its trajectory at a steady velocity. Both its altitude and travel speed must be taken into consideration to calculate this velocity.

Spacecraft in low Earth orbit (LEO) must regain their speed four times each year to counter atmospheric drag, as satellites traverse thicker air during solar maxima which produces greater drag.

Gravity keeps satellites moving constantly around Earth, but too much slowdown or speedup may cause them to spiral away from its center rather than staying on track with its circle path. To prevent this from occurring, orbital velocity must remain stable – as illustrated below for geostationary orbits such as those used by television and communication satellites that remain over one point on its surface.

## Acceleration

Acceleration for satellites orbiting Earth depends on their mass and their distance from its center of gravity; to calculate this acceleration use the formula (m / r) x (2 pi / orbital period).

As an illustration of gravitation at work, let’s imagine we climb to the peak of a mountain and throw an outgoing cricket ball horizontally outward from there – gravity will draw it down in an arc rather than straight. Satellites orbiting their appropriate orbits are subject to similar effects of gravitation, whereby its force exactly balances their forward momentum to keep them flying around circular paths.

As satellites approach Earth, their orbit becomes increasingly affected by atmospheric drag that reduces their trajectory over time and brings them back closer to planet. That is why satellites like International Space Station reside in geostationary orbits rather than polar ones.

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