This paper is based on a thought experiment in which the scenario 'How long would it take a person to go down a slide from the Moon to Earth?' is addressed. After making various assumptions to simplify this experiment, the time taken was calculated to be 74 hours

Howe, Rebecca

Javaid, Rafia

Pitts, Michael J

Scanlan, Fraser R.J

English

University of Leicester Open Journals

Journal of Physics Special TopicsAn undergraduate physics journalA5 3 Sliding in SpaceR. Javaid, R. Howe, M.J. Pitts, F.R.J. ScanlanDepartment of Physics and Astronomy, University of Leicester, Leicester, LE1 7RHDecember 17, 2017AbstractThis paper is based on a thought experiment in which a perfectly rigid slide with zero frictionconnects the surface of the Moon to the surface of the Earth at the closest points. By usingNewton’s Law of Gravity and programming in R, as well as modelling the Earth and Moon astwo stationary points in space, we calculated the time it would take for a person launched from acannon on the Moon to reach the Earth. The time was calculated to be 92 hours.IntroductionEver since men took their first steps on theMoon in 1969 [1], colonising the Moon has beenan area of strong interest in the world of sci-ence. The time taken to slide from the Moonto the Earth has been investigated based on ahypothetical scenario where people travel fromthe Moon to the Earth by being launched ontoa slide that would force them to move on a cer-tain path to prevent them entering into an orbit.This would effectively cause the person to slidefrom the Moon to the Earth.Theory and ResultsTo simplify this scenario, the Moon and theEarth have been modelled as two stationarypoints, and we have made the assumption thatthere is no air resistance or friction acting againstthe person when travelling down the slide. Theinitial step was to find the distance between theEarth and the Moon, rg, at which the net gravi-tational force was zero with respect to the centreof the Moon. This was done using Eq. (1) [2],equating the gravitational forces from the Moonand the Earth as shown in Eq. (2): G = 6.67x 10−11 m3 kg−1s−2 (the universal gravitationalconstant), Mm = 7.35 x 1022 kg (the mass ofthe Moon), Me = 5.97 x 1024 kg (the mass ofthe Earth), m = 60 kg (the mass of the person)[2] and re being the distance from the surface ofthe Earth to the point at which net gravitationalforce is zero.F =GMmr2(1)GMmmr2g=GMemr2e(2)r2er2g=MeMm(3)re + rg = Rtotal (4)Rearranging Eq.(2) for Eq.(3) and substitut-ing in re from Eq.(4), where Rtotal = 384400 kmis the distance between the centre of the Earthand centre of the Moon, resulted with a valueof rg = 3.8 x 107 m, as measured from the cen-tre of the Moon. This value is required in orderto calculate the minimum velocity needed to getfrom the Moon’s surface to the point at whichno gravity is acting on the person.The difference in potential energy between thesurface of the Moon and rg was calculated usingEq. (5), where r is a radius. The energy requiredto travel from the Moon’s surface, r = 1737 kmto r = rg was calculated to be 162000 kJ.U =−GMmmr(5)The kinetic energy equation, Eq. (6), was thenused to calculate the minimum initial velocity,where v is velocity, which came to be 2320 ms−1.E =12mv2 (6)To calculate the time taken for the person totravel from the surface of the Moon to the surfaceof the Earth, the acceleration was required. Tofind the duration of the journey Eq. (7) wouldbe integrated and rearranged for t;dvdt=−GMeR2+GMm(Rtotal −R)2 = a (7)where R is the distance of the person from theMoon and a is the acceleration of the person.As the values of both r and a change withrespect to time, the integral became too complexto solve. As a result, computational methods inR were used to plot graphical representations ofthe scenario (see Figure 1).Figure 1 therefore shows the total travel timedown the slide to be roughly 92 hours.Analysuis and ConclusionDespite this thought experiment not beingpossible to physically conduct as producing africtionless slide between the Earth and Moonis impossible, the total travel time of 92 hoursseems plausible. This is based on the time takenfor the Apollo 11 crew to reach the Moon’s orbit:approximately 76 hours [4].To take this experiment further and acquiremore accurate results, the integral of Eq. (7)could be solved mathematically rather than cal-culated computationally. This would improveFigure 1: Graph of the relationship between the per-son’s distance from the Earth and their travel time. Thered and blue lines are the location of the Moons andEarths surface respectively.accuracy as the computer model only applies de-celeration every 5 seconds which would resultin a lower velocity change than expected duringacceleration and deceleration, meaning a higherinitial velocity would need to be used to give thesame journey time of 92 hours. The spins andorbits of the Moon and the Earth could also beaccounted for, and therefore have more forces in-volved such as the Coriolis effect [5] and friction,which would change the initial velocity neededand alter the time taken to reach the Earth.References[1] Tipler, P. and Mosca, G. Physics for Scien-tists and Engineers 6th ed, (2007)[2] https://nssdc.gsfc.nasa.gov/planetary/factsheet/moonfact.html[Accessed 12 October 2017][3] http://www.nasa.gov/audience/forstudents/k-4/stories/first-person-on-moon.html[Accessed 2 November 2017][4] https://www.space.com/18145-how-far-is-the-moon.html/[Accessed 12 October 2017][5] https://www.nationalgeographic.org/encyclopedia/coriolis-effect/[Accessed 12 October 2017]

A5_3 Sliding in Space

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A5_3 Sliding in Space

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