# Try Landing A Spacecraft On Mercury

 Mercury has almost no atmosphere, so there is no air drag or aerobraking on the spacecraft. The rocket engine must do all the work to slow the spacecraft down and land the spacecraft on the planet.   As the pilot of the spacecraft you must control the direction of rocket thrust relative to vertical and the amount of rocket thrust. The pilot controls the amount of thrust by controlling the rocket engine throttles. The throttles control the amount of fuel flowing into the rocket engines. The amount of fuel flowing into the engines is expressed as the pounds of fuel per second (or kilograms of fuel per second).   A spacecraft, including fuel, weighs 33,000 lbs. (or 15,000 kilograms). Before the spacecraft begins the descent from orbit to the surface of the planet, the fuel in the spacecraft weighs about 19,800 lbs. (9,000 kilograms). The spacecraft is traveling in orbit at a velocity of approximately 5,910 miles per hour (2,642 meters per second) relative to the surface of Mercury. It is traveling in a circular orbit at 250 miles (417 kilometers) above the surface of the planet.

There are 3 possibilities:

• If you open the throttles too far and let too much fuel into the engines you will not land on the surface but will run out of fuel above the planet and then crash onto the surface of the planet.
• If you don't open the throttles far enough you will not slow down enough and will hit the surface of the planet faster than 35 mph (15.6 meters per second) and will hit so hard that you will destroy the spacecraft.
• If you select the right throttle setting, the spacecraft will gradually slow down and land fairly slowly or softly on the surface of Mercury.

You must compute the correct average throttle setting, Q:

Hint: The correct average throttle setting is between 16.0 and 17.5 lbs. of fuel per second (or between 7.27 and 7.95 kilograms per second).

Assume that the velocity of the gases leaving the rocket engines, V = 13,700 ft per second (or 4,150 meters per second). Also, the average deceleration of the spacecraft, D = 9.97 feet per second per second (or 3.02 meters per second per second) if the burn is about 19 minutes.

Q = Average Throttle setting, lbs. of fuel per second (or kilograms of fuel per second).

M = Average Mass of spacecraft during descent, including fuel = 23,300 lbs. (or 10,600 kilograms).

There is very little margin for error. You must compute the right throttle setting almost exactly. Use a calculator to calculate the average throttle setting, Q:

Average Throttle Setting, Q = D x M divided by V = x.xx kilograms per second of fuel.

Go ahead and try different throttle settings, Q, to see what happens: