The part of the sentence "gradually getting closer" is correct and usable in written English.
You can use it when you want to describe the process of two things getting nearer and nearer to each other. For example, "Our two armies were gradually getting closer as they advanced on the enemy's stronghold."
Sound grenades cracked in the distance, gradually getting closer as protesters beat a retreat to the only place in Manama where they now feel safe to gather in numbers.
A road ultimately running from Cusco is gradually getting closer and closer to Boca Manu, and the plan to build the stretch between Boca Manu and Boca Colorado, a town down the River Madre de Dios, to the east, was declared in late 2013 in the "public necessity" and "national interest" by the Peruvian Congress's Commission on Transport and Communications.
And that bridge is gradually getting closer.
As part of this, meteors have been gradually getting closer to the map, and recently hitting it.
Over the course of many years, scientists would gradually get closer to the gorillas, which are now at the point of disregarding their human visitors.
Below the coal seam, ground stresses will gradually get closer to the virgin stresses.
The approach was conducted starting from the more severe conditions of interactions and then gradually gets closer to the interactions taking place in service.
They tweak things, sometimes hardly noticeable little things, in order to gradually get closer to that unachievable "perfect" vision.
This approach allows the audience to gradually get closer to Jimi in the same way and at the same time that Imogen's character gets to know him.
A simple infinite series for is the Gregory Leibniz series: : \pi = \frac{4}{1} - \frac{4}{3} + \frac{4}{5} - \frac{4}{7} + \frac{4}{9} - \frac{4}{11} + \frac{4}{13} - \cdots As individual terms of this infinite series are added to the sum, the total gradually gets closer to, and – with a sufficient number of terms – can get as close to as desired.
When s approaches m, C FANCC gradually gets close to C ANCC.
