Measuring the distance to Mars using simple equipment (UPDATE: first estimates of distance!!)

[cubinator]

Original message:

Spoiler

Hello all,

 

Want to do some science?

On the night of Wednesday, December 7th/Morning of Thursday December 8th, Earth's Moon will pass directly in front of Mars for observers in the highlighted areas of this graph. The event coincides with the opposition of Mars, when it should (theoretically!) be at its closest point to Earth.

About 30 minutes later, the Moon will pass in front of the star k Tauri, which has an apparent magnitude of approximately 5.75. This is a fairly dim star, and I'm not sure if it will be easily visible through a telescope when it's right next to the full Moon. But if it is, then I believe that we can use the amount of time between the Mars occultation and the k Tauri occultation to calculate the distance between Earth and Mars. 

The only equipment necessary is a telescope powerful enough to see the disk of Mars and the background star, an accurate clock, and a watchful eye. The other helpful thing would be if you live as far away from Minneapolis, USA as possible while still being able to observe the event! If you live in the general vicinity of France, Britain, or Germany and own a telescope you are in the perfect place to help me out!  What I would ask of a fellow amateur astronomer is to get up early on Thursday morning (sorry!), set up your telescope in the area mentioned above, and record the exact time of day (hh:mm:ss.xx) of (1) the moment Mars just begins to touch the Moon, (2) the moment Mars first completely disappears behind the Moon, and (3) the moment the star k Tauri passes behind the Moon (this one happens more or less instantaneously).

If you live in more or less the area mentioned above and would be willing to go outside at 4:30 AM on Thursday with only two days' notice, please send me a message!

I also think the observation could work from the West Coast of North America i.e. California up to Vancouver but it's just not as much distance so it might be a little harder to get a meaningful measurement. So if you're an American who might be able to help, the good news is the event is Wednesday night, not Thursday morning. But we may not get as much resolution in our result.

 

Thanks for reading this, and if you're in the right place and willing to help me out please send me a DM!

On the night of Wednesday, December 7th/Morning of Thursday December 8th, Earth's Moon passed directly in front of Mars for observers in the highlighted areas of this graph. The event coincided with the opposition of Mars, when it should (theoretically!) be at its closest point to Earth. 

Using the difference in timing of the event at different locations around the Earth, it should be possible to calculate the distance to Mars using parallax. Thanks to the effort of a few of our forum members, timing data was gathered from three distant points across the world!

California:

Mars Disappearance: 

Halfway ~18:34:54.3 PST = ~02:34:54.3 UTC
Fully Set 18:35:18.4 PST = 02:35:18.4 UTC

Mars Appearance:

Halfway ~19:35:39.5 PST = ~03:35:39.5 UTC
Fully Risen 19:36:02.6 PST = 03:36:02.6 UTC

Minnesota:

Mars Disappearance:

Beginning 03:03:10.7 UTC
Fully Set 03:03:58.0 UTC

Mars Appearance:

Beginning 04:09:27.7 UTC
Fully Risen 04:10:06.8 UTC

Derbyshire:

Mars Disappearance:

Beginning 04:57:02:82 UTC
Fully Set: ---

Mars Appearance:

First Seen 05:57:11:09 UTC
Fully Risen 05:57:36:71 UTC

Thanks to @K^2 and @Starshot for participating and providing this data!

I will not get around to the math on this right away because of other obligations, but I will probably have some results to post here by the end of the year!

Edited September 9, 2023 by cubinator

[JoeSchmuckatelli]

Fun! - GL!

[cubinator]

I did a similar experiment a few years ago with fellow forum user @LaydeeDem where we used parallax to measure distance to the Moon. 

We got a pretty good estimate of its distance, and this time it's not necessary to take an image like we did last time, just to record the timing between certain events. I think the parallax of the Moon will be irrelevant for the Mars experiment calculations because we are only using the Moon's angular velocity across the sky as a basis for other timing measurements that give us Mars's position against the background stars. 

[SunlitZelkova]

6 hours ago, cubinator said:

I also think the observation could work from the West Coast of North America i.e. California up to Vancouver but it's just not as much distance so it might be a little harder to get a meaningful measurement. So if you're an American who might be able to help, the good news is the event is Wednesday night, not Thursday morning. But we may not get as much resolution in our result.

I would, but it’s basically constantly cloudy in Oregon and Washington until March 

[Nazalassa]

13 hours ago, cubinator said:

4:30 AM

I have class at 8 AM sooo... I guess I'll rather sleep :)

(sorry)

[K^2]

California coast. We are likely to get haze at that time, and I'm not sure if I even have a working telescope anymore. But if I can, I'll give it a try.

[cubinator]

On 12/6/2022 at 10:44 AM, Nazalassa said:

I have class at 8 AM sooo... I guess I'll rather sleep

(sorry)

A more perfect opportunity is unlikely to come by chance, and it's a rare experience to begin with, but I can't make you do it. I know the value of sleep too. 

10 hours ago, K^2 said:

California coast. We are likely to get haze at that time, and I'm not sure if I even have a working telescope anymore. But if I can, I'll give it a try.

Alright, maybe you can let me know an hour or two in advance whether you think you'll be able to make the measurements. If you can catch the emergences but not the disappearances that would be just as helpful.

[Starshot]

Brit with telescope here, I'm willing to give it a go. Current weather forecast is 15% cloud at that time, so may not be possible but I'm up for trying.

[K^2]

Yeah, I'll need to check the weather a bit closer to the time of. Last night, I could see the Mars, but not k Tauri, and this method only works with both reference points, I think?

Precision's going to be tight. Proximity of the Moon means that the occlusion of k Tauri is going to happen at different moments in time, and for me, the Moon is still going to be low on the horizon, so we're not getting anywhere near the 2,500km separation. And you'll need to take into account how the Earth rotates between the two occlusions. I'm not sure you'll get the correct order of magnitude with ±1s... But I'm willing to give it a try, weather permitting.

I also need to find a suitable observation site. I'm not sure I'll have a clean enough view of the East from the place I had in mind.

Edit: Right now it looks like it will be a bit cloudy, which is likely to make things near horizon completely unobservable.  Emergence might be more viable, since that should happen higher up in the sky. I'll keep you updated.

Edited December 7, 2022 by K^2

[cubinator]

32 minutes ago, K^2 said:

Yeah, I'll need to check the weather a bit closer to the time of. Last night, I could see the Mars, but not k Tauri, and this method only works with both reference points, I think?

Precision's going to be tight. Proximity of the Moon means that the occlusion of k Tauri is going to happen at different moments in time, and for me, the Moon is still going to be low on the horizon, so we're not getting anywhere near the 2,500km separation. And you'll need to take into account how the Earth rotates between the two occlusions. I'm not sure you'll get the correct order of magnitude with ±1s... But I'm willing to give it a try, weather permitting.

I also need to find a suitable observation site. I'm not sure I'll have a clean enough view of the East from the place I had in mind.

There may be a few ways I could make this work with fewer observations, but all of these measurements can be helpful. The time it takes Mars to 'set' and 'rise' should be around 30 seconds, so I think if we are measuring a difference which should be a few seconds we might just get something. I think the rotation of Earth might actually help us out a little here too, by increasing the distance between our first observations by a little bit.

You should have the Moon about 20 degrees up at disappearance, and rising.

42 minutes ago, Starshot said:

Brit with telescope here, I'm willing to give it a go. Current weather forecast is 15% cloud at that time, so may not be possible but I'm up for trying.

Thanks so much! That would be fantastic!

As for the timing measurements, I am thinking of recording myself calling out times on my phone, because I won't be able to reliably hit a stopwatch button on the screen while I'm looking through the telescope. I'll call out the time of day at some point in the recording so I get a basis for the other timings.

[cubinator]

I also suggest using an online service like https://time.is/ or https://www.time.gov/ to verify the accuracy of your clock.

[K^2]

There are some NTP-based clock apps on the Android store. I plan to just take screenshots with that app open, since that's probably the easiest way to time it for me.

[cubinator]

4 minutes ago, K^2 said:

There are some NTP-based clock apps on the Android store. I plan to just take screenshots with that app open, since that's probably the easiest way to time it for me.

That's a good idea, I may have to try that.

[Starshot]

22 minutes ago, K^2 said:

There are some NTP-based clock apps on the Android store. I plan to just take screenshots with that app open, since that's probably the easiest way to time it for me.

AtomicClock: NTP Time has an settings option where tapping anywhere on the screen freezes clock on click, so can click on event and then screenshot or write down the time when screen frozen.

[K^2]

1 hour ago, Starshot said:

AtomicClock: NTP Time has an settings option where tapping anywhere on the screen freezes clock on click, so can click on event and then screenshot or write down the time when screen frozen.

Perfect! That's the one I have installed, too. It's a neat app. Didn't know about this feature, though. Thanks.

Weather update: Haze up to about 30° in the East. The moon came over the horizon now and is clearly visible, but I can't see anything else. Of course, there's still quite a bit of sunlight making things a lot worse. So I'll check again in another 30 minutes or so to make a final go-no-go for trying to gain occlusion data. It should be better on the flip side, but I'm very likely to miss k Tauri showing up on the other side. I'll try to get a better estimate for when exactly I should expect that, and this might help me time it, but I might be very limited in ability to provide helpful data points.

[cubinator]

I set up my telescope and I haven't been able to spot k Tauri in the Moon's glare. I think that star's not going to be much help. 

I think the calculation should still be possible with timing of just Mars and parallax across Earth's surface, if we use the known distance to the Moon and Moon's angular velocity. It most likely won't be as accurate, but it might be good enough.

We can know the Moon's angular velocity across the celestial sphere from its period, as well as the Moon's angular size, and because we're effectively measuring Mars' angular velocity against the Moon we can find Mars' angular velocity against the celestial sphere. We just need to take a guess at the timing of Mars' occultation on different parts of Earth based on the distance to the Moon and figure out the difference with what we observe.

Edited December 8, 2022 by cubinator

[sevenperforce]

I can't help because I'm not very far from Minneapolis and my telescope isn't very big but this is such an awesome thread.

[K^2]

My stand sucks and I had too much wobble, so I missed the initial contact point. Mars was about half-way at 18:34:54.3 PST and fully set right around 18:35:18.4.  I'm going to try and catch the rising time to provide additional data. Hopefully, I'll have it a bit more steady for that. (And I'll DM you the location, since I had no chance of sighting 98 k Tauri anyways, and Mars was visible from my front yard.)

[cubinator]

Mars occlusion from Minnesota:

1st Contact 03:03:10.7 UTC

2nd Contact 03:03:58.0 UTC

This is 1 minute later, and slightly longer lasting than Stellarium predicted. Perhaps I should make sure my location is set precisely.

Edited December 8, 2022 by cubinator

[K^2]

Wind-induced oscillations are not a good indicator for a telescope mount. 

So again, closer to mid-point around 19:35:39.5 with separation at 19:36:02.6. And don't ask me to estimate an error, because it was definitely not amazing for what you're trying to do. v_v

Kind of made me want to buy a telescope with a tracking mount, though...

[cubinator]

Thanks so much for the observation @K^2!

[cubinator]

I have my reappearance times!

First Appearance 04:09:27.7 UTC

Fully Detached 04:10:06.8 UTC

What an amazing experience! I'm definitely going to go watch Mars for a little while longer, because I can see an amazing amount of detail!

[Starshot]

Mars Occultation from Derbyshire:

1st contact 04:57:02:82 UTC

Didn't get full disappearance, sadly.

Should be able to get reappearance in about half an hour.

Edited December 8, 2022 by Starshot

[Starshot]

Mars Reappearance:

1st sighting 05:57:11:09

Fully Detached 05:57:36:71

Fully detached is probably the more accurate of these observations.

Will DM you the location

[cubinator]

Thanks greatly @Starshot! I hope you get some sleep at some point!