note: for the purposes of launch statistics one should probably use the smaller of the two numbers below; the insertions of the "000" for debris items should not count.
Celestrak
offers a copy of at Satcat from which a tabulation of space objects can be gleaned:
The legacy text format (uses column numbers instead of the new CSV format) is as follows:
001-011 International Designator
Launch Year (001-004)
Launch of the Year (006-008)
Piece of the Launch (009-011)
So for each year we should be able to count the number of unique "Launch of the year" values exist, and compare it to the highest value to see if they agree.
They do except in 1971 and 2014 where there's a difference of one more launch of the year than the highest launch number. This happened because someone inserted a value of 000
for launch of the year:
1971-000E 05310 D US UNKNOWN 1 DEB US 1971-01-01 AFETR 1990-09-26 1436.7 1.2 35795 35763 N/A
2014-000A 40328 UNKNOWN LDS DEB CIS 2014-01-01 PLMSC 710.6 70.5 32069 7930 0.0030
Here's a plot of the data, and the raw numbers below. Please note that it is not accurate for this year 2020 because the year isn't over yet.
inelegant script for sorting and plotting https://pastebin.com/GykNkE5Q
tabulated results (year 2020 is incomplete!)
1957 2 2 True
1958 8 8 True
1959 14 14 True
1960 19 19 True
1961 35 35 True
1962 72 72 True
1963 55 55 True
1964 87 87 True
1965 112 112 True
1966 118 118 True
1967 127 127 True
1968 119 119 True
1969 110 110 True
1970 114 114 True
1971 121 120 False
1972 106 106 True
1973 109 109 True
1974 106 106 True
1975 125 125 True
1976 128 128 True
1977 124 124 True
1978 124 124 True
1979 106 106 True
1980 105 105 True
1981 123 123 True
1982 121 121 True
1983 127 127 True
1984 129 129 True
1985 121 121 True
1986 103 103 True
1987 110 110 True
1988 116 116 True
1989 101 101 True
1990 116 116 True
1991 88 88 True
1992 95 95 True
1993 79 79 True
1994 89 89 True
1995 74 74 True
1996 73 73 True
1997 86 86 True
1998 77 77 True
1999 73 73 True
2000 82 82 True
2001 58 58 True
2002 62 62 True
2003 61 61 True
2004 53 53 True
2005 52 52 True
2006 63 63 True
2007 65 65 True
2008 67 67 True
2009 75 75 True
2010 70 70 True
2011 80 80 True
2012 75 75 True
2013 78 78 True
2014 91 90 False
2015 83 83 True
2016 83 83 True
2017 86 86 True
2018 112 112 True
2019 97 97 True
2020 87 87 True
United Nations
Ars Technica's SpaceX Starlink engineers take questions in Reddit AMA—here are highlights included a reader poll when I viewed it, screen shot below. It said:
The United Nations Office for Outer Space Affairs monitors and logs objects, including satellites, launched each year.
Their home page is at https://www.unoosa.org/ and there is a page called Outer Space Objects Index
But this just looks like an attempt to make a "UN Satcat clone"