How fast the Sun travels
The Sun appears to complete the zodiac once a year, so it averages a shade under one degree a day. The rate is not constant. The Earth's orbit is slightly elliptical and the Earth is near its farthest point from the Sun in early July, so around this date the apparent motion is at its slowest, a touch over fifty seven minutes of arc in twenty four hours.
That still amounts to close to a full degree between midnight and midnight. Someone born at two in the morning and someone born at eleven at night on the same 9 July, in the same place, have solar longitudes that differ by most of a degree.
The year matters too, but less
Sampling noon from 1930 to 2035, the Sun on this date fell between roughly sixteen and a half and just under eighteen degrees of Cancer. The spread across the whole century is about a degree and a half, which is only slightly larger than the spread across one day.
Both effects trace back to the calendar. A common year is a quarter day short and leaves the Sun about six hours late at any given longitude, while a leap February pulls it back by around a day. The near cancellation is what keeps the century range so narrow.
When the difference of a degree matters
For naming the sign it never matters here. Seventeen degrees of Cancer is thirteen degrees from the nearest boundary, so no hour of this date could tip it into another sign in any year of the sample.
It matters for anything measured to the degree. Aspects between planets are counted in degrees with tight allowances, and a placement close to a face boundary can sit on either side depending on the hour. On this date the second face runs to twenty degrees, so the daily motion never crosses it, but the same arithmetic on a date three days later would.
It is also worth being concrete about scale. The Moon is at most two signs on any single 9 July and any of the twelve across the sampled years, while the ascendant is all twelve within one day, changing about every two hours and shifting a degree every four minutes. Those are the placements that actually separate two people born on this date. The Sun is the part they share, which is why it carries the least information about either of them.
What to do with an unknown time
Where the hour is not known, calculations default to noon. On this date that is a safe default for the sign and a reasonable one for the solar degree, since the worst case error is half a degree either way.
It is not safe for the Moon, which can change sign inside a single day, nor for the ascendant, which turns through all twelve signs in twenty four hours. The widget above uses the hour and the birthplace where you have them, and reports both your solar degree and the distance from it to the nearest sign boundary.
The other thing worth noting on a date this far into a Moon ruled sign is that the sign's ruler is also the least predictable body in the chart. Cancer belongs to the Moon, so the planet the tradition would send you to first for the meaning of the chart is the one moving thirteen degrees a day. A calendar date fixes the Sun tightly and leaves the ruler of its sign almost entirely open, which is an unusual arrangement and specific to this sign.
Questions people ask about this
What sign is 9 July?
Cancer, settled in every year sampled. Both the Cancer and the Leo ingress are far enough away that no hour of this date comes close to either.
How much does the Sun move in a day?
Just under a degree on average, and slightly less than that in early July because the Earth is near the far point of its orbit and the apparent motion slows.
Does my birth hour change my sun sign here?
No. It shifts the degree by up to about a degree, which is nowhere near enough to reach a sign boundary from the middle of Cancer.
What degree of Cancer applies to this date?
Around sixteen and a half to eighteen degrees at noon depending on the year, with the hour of birth moving it within roughly a degree of that.
Which decan is 9 July?
The second decan of Cancer, from ten to twenty degrees, ruled by Mercury in the Chaldean order and by Mars through Scorpio in the triplicity scheme.
When would the hour change a decan?
Only when the position sits within about a degree of ten, twenty or thirty degrees. This date runs several degrees clear of the twenty degree edge in every sampled year.