Determining the exact size of the Moon's apparent diameter 100 million years ago is a complex task that involves several factors, including the Moon's orbital parameters and the Earth-Moon distance at that time. However, I can provide you with an estimate based on the current understanding of lunar evolution.
Over the past 100 million years, the Moon's orbit around the Earth has gradually been increasing due to tidal interactions. This means that the Moon was closer to the Earth in the past. The rate of the Moon's recession is approximately 3.8 centimeters per year.
If we assume a constant rate of recession over the past 100 million years, the Moon would have been about 38 million kilometers closer to the Earth than it is today. This corresponds to a decrease in the Moon's average distance from the Earth of approximately 2.6 Earth radii.
To calculate the change in apparent diameter, we need to consider the angular size formula:
Angular Size = (Diameter of the Object) / (Distance to the Object)
Assuming the current average distance from the Earth to the Moon is approximately 384,400 kilometers and using the estimated change in distance, we can calculate the change in angular size.
Current Angular Size = (Diameter of the Moon) / (Current Distance to the Moon)
New Angular Size = (Diameter of the Moon) / (Current Distance to the Moon - Change in Distance)
The angular size of the Moon is approximately 0.52 degrees (or 31 arc minutes) when it is at its closest point to the Earth (perigee), and it is about 0.50 degrees (or 30 arc minutes) when it is at its farthest point (apogee).
Using these values, we can estimate the change in apparent diameter. However, please note that this calculation assumes a constant rate of recession, which might not hold true over such a long timescale.
Based on these approximations, the Moon's apparent diameter 100 million years ago would have been slightly larger than it is today. The exact increase in angle would depend on the precise rate of recession over that time period.