New Horizons flyby of Pluto [updated for Ultima Thule]

[fizzy]

Well, I found a gravity bug in my method, yielding somewhat different numbers.

My gravity number is 4 times larger than yours at the Thule end.
Even discounting the gravity from Ultima, my value is still 3 times higher than yours.
g = 1.5e15 kg * 6.674e-11 / (7000 m)^2 = 0.002043 m/s^2

0.002043 / 0.0007 = 2.9

What am I doing wrong?

You are using billiard ball physics but your "centre" of mass seems to be at the point they touch.

If you want to simply to two point masses they are separated by 7+9.5km
If you want the effect of one mass at the outside to the other it's its radius plus the diam of the other.

BTW inverse square law can only be applied "far field" , ie. where the diameters are much smaller than the separation between them.

 

[mfb]

Inverse square law is exact everywhere outside of spherically symmetric objects (within Newtonian mechanics). Didn’t pay much attention to that discussion part so far but if there is still something unclear I can have a look.

 

[fizzy]

"Inverse square law is exact everywhere outside of spherically symmetric objects"
It is good enough for a first approximation but it is certainly not exact.

Consider a test mass one radius from a spherical body. Work out the contributions form two points diametrically opposed on the surface, once is distant by r , the other by 3r. Compare that to the same masses placed a the centre of mass.

1/r^2+1/(3r)^2 = 2/(2r)^2 ??

A similar inequality and of the same sign will apply for all pairs of points symmetrically placed either side of the plane through the c.o.m. and perpendicular to the line joining the test mass and the centre. Summing all such pairs to represent the whole shows the inequality holds for the whole body.

The inaccuracy reduces as the separation becomes much larger than the diameter of the sphere.

 

[mfb]

It is exact. You can't limit the calculation to two points, you have to integrate over the whole shell. Do it and see what you get.
Alternatively: It is a direct consequence of Gauss' law.

This is a well-known result from classical mechanics and not the topic of this thread. If you have more questions about it please start a separate thread.

 

[fizzy]

fair point:
https://www.physicsforums.com/threads/is-inv-sqr-law-exact-near-to-a-spherical-body.963631/

 

[OmCheeto]

I also started another thread on the math problem: https://www.physicsforums.com/threads/net-forces-on-ultima-thule.963691/

 

[OmCheeto]

And, we're back in business.

Not sure how long it will take to download the next image. I guess it depends on how big the file is.

 

[Borg]

Could you post the link to that page, Om?

 

[OmCheeto]

Could you post the link to that page, Om?

https://eyes.nasa.gov/dsn/dsn.html

Btw, it's possible they were just checking for a signal when I checked, and got nothing but noise.
Currently, only 3 of the 12 dishes are in use, and New Horizons is not one of them.

 

[mfb]

Canberra (43) is receiving data from New Horizons right now. 2 kb/s downlink at 8.44 GHz, 500 b/s uplink at 7.18 GHz.

Edit: Canberra tweeted it, too

 

[glappkaeft]

New images released: http://pluto.jhuapl.edu/News-Center/News-Article.php?page=20190115

Better images will be availible in late Februari: https://twitter.com/AlanStern/status/1085236157565276162

 

[mfb]

We got a new picture now already.

Article

Full resolution

 

[DrClaude]

Pancakes!

https://apod.nasa.gov/apod/ap190211.html
http://pluto.jhuapl.edu/News-Center/News-Article.php?page=20190208