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Landing spacecraft on Mars and other planets: An opportunity to apply introductory physics
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Image of Fig. 1.
Fig. 1.

Artist's conception of the entry of Curiosity into the atmosphere of Mars. NASA/JPL-Caltech image PIA 14835.

Image of Fig. 2.
Fig. 2.

Deceleration as a function of time since atmospheric entry (gray line) during the arrival of Pathfinder at Mars in 1997. The black line shows an exponential fit to a portion of the gray curve. This fit, which has a characteristic timescale of 4.3 s, illustrates that Eq. (5) holds well for this mission. In the data, a maximum deceleration of 155 m/s occurs at 114 seconds, parachute deployment occurs at 209 s, and first impact occurs at 336 s. (Data source: NASA Planetary Data System dataset MPAM_0001.)

Image of Fig. 3.
Fig. 3.

Prior to parachute deployment or retrorocket ignition, the speed of a spacecraft of mass depends on the mass of atmospheric gas that is swept up by the spacecraft. The six solid lines show how the ratio of speed to initial speed depends on altitude (in units of scale height ) for different values of . Here is the mass of a vertical atmospheric column above altitude  = 0 that has an area equal to the spacecraft area, and is the angle between the spacecraft velocity and the vertical, so that is the mass of atmospheric gas swept up by the spacecraft by altitude  = 0.

Image of Fig. 4.
Fig. 4.

A view from Mars orbit of Curiosity descending on its parachute. NASA/JPL/University of Arizona ESP_028256_9022.

Image of Fig. 5.
Fig. 5.

Closeup view of the damaged Genesis capsule after its return to Earth. NASA/JPL-Caltech.

Image of Fig. 6.
Fig. 6.

The altitude and speed of a spacecraft descending on a parachute at terminal velocity are related to the atmospheric scale height , the terminal velocity at parachute deployment , and the time since parachute deployment. Here is the altitude of parachute deployment so is the change in altitude since parachute deployment; similarly, is the time of parachute deployment so is the time since parachute deployment. We plot dimensionless altitude [ , solid line] and dimensionless velocity ( , dashed line) as functions of dimensionless time since parachute deployment [ ].


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Table I.

Information on several planetary atmospheres. Values are at the 10 Pa pressure level for Jupiter and the surface for all other objects. Scale heights are calculated using . (Data from Ref. )

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Table II.

Information on several spacecraft. (Data from Ref. and sources therein.)


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Landing spacecraft on Mars and other planets: An opportunity to apply introductory physics