Up, Up, and Away

To the Red Planet

• We must know the length of the planet's year, its orbital speed, and its exact position. The spacecraft must be aimed not to the planet, but to where the planet will be nine months in the future.
• We must also choose a time when Mars is close to the Earth; these opportunities, or launch windows, occur every two years.
• Our Earth travels around the Sun at a faster speed than Mars does. The spacecraft will already have the 107,000 kilometers per hour (66,500 miles per hour) speed of Earth, whereas Mars moves at only 86,900 kilometers per hour (53,900 miles per hour). To allow for this, mission planners must launch the spacecraft when Mars is ahead of Earth in its orbit. Then the spacecraft will catch up to Mars because of the higher velocity provided by Earth.
• The spacecraft must break free of the Earth's gravity. This requires a speed, known as the escape velocity, of at least 40,300 kilometers per hour (25,000 miles per hour) with respect to Earth. At a lesser speed, the craft would go into a highly elliptical orbit around Earth. Once the craft breaks out of orbit around Earth, it goes into orbit around the Sun.

The Hohmann transfer orbit from Earth to Mars is very curved (see diagram) because the 107,000 kilometers per hour of the Earth's orbital motion about the Sun combines with 41,200 kilometers per hour imparted by the rocket engines. In a similar fashion, a bomb dropped from a plane makes a curved path due to the speed of the plane and the gravity of Earth. Moving in a straight path from Earth to Mars would take an enormous amount of fuel.

Come take a trip around Mars. To get to Mars, first launch yourself into orbit around Earth. Then fire your rockets in the same direction that Earth is moving around the Sun. A speed of about 42,000 kilometers per hour will be enough to escape the Earth's gravity and, when added to the Earth's orbital speed around the Sun, put the spacecraft on a Hohmann transfer orbit to the Red Planet. If you time it right, you'll arrive at the orbit of Mars when the planet is there. At that point, fire the rockets to match your speed to that of Mars. By the way, when you get there, send us a postcard.

Eight months after launch, the spacecraft arrives at Mars, where it must slow down enough to be captured by the martian gravity. The escape velocity of Mars is 18,000 kilometers per hour (11,000 miles per hour), a good deal slower than the escape velocity of Earth, because gravity on Mars is weaker (see table). In the past, Mars-bound space probes have gone into Mars orbit by firing retrorockets to slow down.

Engineers are now working on a technique that does not require a retrorocket. Called aerocapture or aerobraking, the technique aims the craft into the planet's outer atmosphere to slow it down by atmospheric drag. This technique was shown in the movie "2010'' when the Russian spaceship Leonov went into Jupiter orbit. In fall 1994, mission controllers used aerobraking to circularize the orbit of the Venus probe Magellan. Relieved of the need to carry rocket fuel, an aerobraked probe could instead carry twice the payload. Aerocapture might prove dangerous for a manned Mars mission, though, for it would suddenly subject the astronauts to 6 to 8 gs after they had spent months in zero-g. Six to 8 gs would cause a 150-pound astronauts to weigh 900 to 1,200 pounds.

Thanks for the Lift

But because the planet is orbiting the Sun, the process is not symmetrical. If mission controllers choose the right approach path, the space probe can have a net gain or loss of speed. The most famous gravity assist sent Voyager 2 from Jupiter to Saturn, Uranus, and Neptune. With each flyby, the path of Voyager was bent and its speed was increased in the direction of the planet's motion. The Galileo probe [see "Here Is My Journey's End,'' The Universe in the Classroom, Fall 1995] swung by Venus once and Earth twice to gain the momentum to reach Jupiter.

The only problems with gravity assists are that they increase the flight time and require waiting for the planets to be lined up in the proper configuration. Voyager made its journey from Earth to Jupiter in just under two years without an assist; Galileo took a little over six years using the assists.

Perhaps one day humans, too, will fly to the planets -- and beyond. But the farther a craft must go, the more problems it will encounter. To escape the Sun's gravity, a starship launched from Earth would have to go at 152,000 kilometers per hour (94,000 miles per hour). Even at that respectable speed, the stars would seem impossibly distant. Stars lie at distances measured in light-years. A light-year is the distance that light travels in one year -- about 9.6 trillion kilometers (5.9 trillion miles). At the above velocity, it would take 30,000 years to reach the nearest star.

Increasing the speed would require special, as-yet- undeveloped types of rocket engine to minimize the amount of fuel the starship would need to carry. By accelerating at 1 g for several months, a starship could make it to the nearest star and back in 30 years. But for this journey, even a "Star Trek''-style antimatter engine would consume 40,000 tons of fuel per ton of payload. The odds seem insurmountable, but remember that just a half century ago, few people seriously thought that we could visit space at all.

JAMES J. SECOSKY is a science teacher at Bloomfield Central School in Bloomfield, N.Y. He used to teach a summer course for kids, "How to Drive the Space Shuttle.'' For more information on space travel, an excellent resource is Thomas Damon's Introduction to Space, published by Krieger Publishing.

How Fast Do You Have to Go?

The first column in this table gives the velocity of a satellite in low orbit -- that is, an orbit near to the surface of the body. This is the highest speed a satellite of that body can have; farther away, a satellite orbits at a slower speed. The second column gives the escape velocity. Any rocket launched from the surface with this velocity will break free of the body's gravity altogether. Do you notice anything about the two columns of numbers?

<< previous page | 1 | 2 | 3 | 4 | next page >>

back to Teachers' Newsletter Main Page