Is it possible to extract the value of g (the gravitational constant of a planet) from a video clip?

Question

I raise this question to the Physics geeks out there because there's a claim from a certain tech Y! group member that he was able to calculate or extract g = 9.8 m/sec/sec from a particular NASA video clip. This is no other than the Apollo 16 Lunar Rover video clip, which shows the Lunar Rover being driven by Astronaut John Young as it vigorously kicks up dust in the lunar landscape. My challenge to you is to either refute or verify this claim. Refutation is good for it will dispel any doubt on the veracity of the Lunar Rover video. However, verification of this calculation will surely cast doubt on the truthfulness of the whole mission and reveal something that has the potential to "shake up the whole world."

for the tech Y! group claim and the source of the NASA video clip, please refer to the links below. Many thanks!

http://tech.groups.yahoo.com/group/apollo_hoax/message/128
http://www.hq.nasa.gov/office/pao/History/40thann/mpeg/ap16_rover.mpg

Answer 1

Bingo!



What an interesting question this is! I may not be able to provide an outright verification/refutation of the problem at hand but I have definitely found a 'humongously riveting' special problem for my undergraduate Mechanics/Kinetics course this coming semester. Oh boy, am i excited to download that video clip already!!!



Hey Prof. Zikzak! I really like your explanations, but you're point #2 lacks another important item to be considered for the experiment, and that is the VELOCITY of the dust at the point of being kicked up by the Lunar Rover wheels. The whole thing should be treated as a PROJECTILE MOTION problem and, as such, the velocity of the dust at 'take-off' should be measured as well. This can be obtained by calculating the rotational velocity of the wheels, i think.



In addition, the parabolic trajectory may not be a confirmation of the motion happening in vacuum, but more of a confirmation of the dust taking the path of a projectile in motion.



Whoopee!!!

Answer 2

I wasn't going to answer, but Ian is clearly wrong. Point by point,



(1) It makes NO DIFFERENCE WHATSOEVER that you do not know the masses involved. The acceleration due to gravity on the surface of the Moon is g, with g = GM/R^2, a constant, regardless of the mass of the dust. g does depend on the mass and radius of the Moon, but that is the WHOLE POINT. Measure the acceleration of the dust and you have measured g.



After doing the experiment, you compare this measurement with the theoretical value of GM/R^2 for the moon.



(2) Oblique angles make little difference. The only important measurements are: (a) the height of the arc of dust, and (b) the time to fall from that height. The height can be estimated by comparing to the height of the tire, or the height of the astronaut, which are not affected by the angle of the camera to the buggy.



(3) The frame rate makes no difference. There will be many multiple frames between dust height and dust hitting the ground. The time measurement will be accurate to about 1/30 of a second, correct. The total time in the experiment will be several seconds, for order of 1% error. This is NOT "enormous" by any means. The primary source of error will be measuring the height of the dust arc. Welcome to the world of experiment.



(4) Again, camera angles make no difference as long as the height of dust can be estimated by comparison to nearby objects.



There will be experimental error, particularly in measuring the maximum height of the dust. EVERY experiment has experimental error. If you abandoned every experiment that had error, you would never do an experiment.



EDIT: You could, if you wished, measure the position of a particular dust clod in each film frame, which perhaps is what Ian is getting at. This is wholly unnecessary for measuring g, but it might be useful in confirming that the trajectory was a parabola, thus eliminating air resistance as a factor, showing that the motion is in vacuum. (Although you don't really need to measure the dust clod's every position for this; you could simply measure the shape of the entire arc of dust in a single frame, if it all emanated from the same point with equal velocity, for instance). Ian's objections generally do not hold any water here either, as a parabola seen from any angle is still a parabola. Objection (4) is more relevant, but the optics of the cameras are well-known and should be included in the geometry.



I will abandon this experiment, however, because the Apollo-deniers have no interest in the truth. Any evidence you present will be denounced as fake. It's a waste of time.

Answer 3

It is impossible to calculate and here's why.



1) The basic mathematics involved: - Newtons Universal law of Gravitation.



F = GMm/R^2



where:

F is the force of attraction between two objects

G is the universal gravitational constant; G = 6.67*10-11 N-m2/kg2. The units of G can be stated as Newton meter-squared per kilogram-squared or Newton square meter per square kilogram.

M and m are the masses of the two objects

R is the distance between the objects, as measured from their centers

GMm/R^2 is G times M times m divided by R-squared



Why you can't calculate it from a video clip.



1) You have no direct way of measuring the

respective masses of the objects involved.



2) in respect of the video in question (not seen it but i'm sure I know which clip it is) the vehicle is not parallel to the camera, thus rendering it almost impossible to accurately calculate the respective distances between the rover, dust and ground plane particularly at oblique angles relative to the camera.



3) In a normal video the timeframe simply isn't accurate enough for accurate time measurement better than approx 1/30th of a second. Thus inducing enormous errors in to the calculation. (this is based on a 29-30fps rate).



4) The field of view of the camera that took the video is unknown, nor from a video clip alone can you deduce any accurate measurement unless there is an accurate measurement scale or 3D grid imposed on the clip at the time of recording. Not knowing the field of makes all distance measurement at best a rough approximation and at worst an outright guess.





Addendum.

In response to the two posters below me:



Yes you can calculate it if you bring in external information that is NOT included in the video clip.



However, the posters original question is actually "Is it possible to extract the value of g (the gravitational constant of a planet) from a video clip?"



It is NOT possible unless you know the dimensions (either mass or length (or distance to from camera), of one objects and the angle and distance between it and a second object in order to calculate the necessary 3D mapping points to measure other objects in frame.

The reason for this is you are attempting to solve a 3 Dimensional problem based on a 2 Dimensional view.



Now going back to the original posters question, re the lunar lander. If you do not know the gravity constant then the arguement above stands. If you bring in external data such as camera information you can calculate it if the requirements in my addendum are met.



Finally for the original poster. Astronomers measuring an unseen planet orbiting another sun use a method where they measure the 'wobble' of the star, and from that calculate the mass required to induce the amount of wobble in said star. In order to make this measurement the astronomer has to know the distance to the star and the mass of the star reasonably accurately.

Answer 4

It's actually very easy to calculate.

If you know a given height, you can time the time taken for an object to fall.

We know the acceleration due to gravity on the Moon, it is 1/6th that of Earth so it's 9.8/6=1.6m/s²



Using S=Ut+½at² ....................since U=0



t²=S/½a



On Earth, an object falling from 20cm will hit the ground in 0.2 seconds.

On the Moon the same fall will take 0.5 seconds.



At a film speed of 25 frames per second the Earth fall will last for 5 frames.

The Moon fall will last for 12.5 frames.

A pretty obvious difference. Anyone who can't tell the difference is blind or stupid.