During his recent space shuttle on the moon, Rajesh used his mobile phone to take a photo of the planet Earth while $100$ km above it$.$ The photo was $10$ MB in size. Suppose that he wants to upload this photo to his twitter page, and is trying to decide whether to do it immediately during his shuttle flight, or after he lands back on Earth $10$ minutes later.

$($Note: $1$ Kbps $=10^3$ bits per second, $1$ Mbps $=10^6$ bps$,1$ MB $=2^20$ Bytes, and $1$ Byte $=8$ bits$).$

a$)$Assuming that his cellular provider offers signal coverage that reaches the shuttle, with a data rate of $100$ Kbps $($and reasonable roaming charges$),$ approximately how long will it take to upload the photo while still on the shuttle? Show your work.

b$)$ Assuming that his cellular provider offers signal coverage at the shuttle landing area, with a data rate of $1$ Mbps$,$ approximately how long will it

take to upload the photo immediately after landing? Show your work

c$)$ Considering that it will take $10$ minutes before the shuttle lands, which of the foregoing two approaches is faster, and by how much?