If a galaxy is 9.0 Mpc away from Earth and recedes at 488 km/s, what is H0 (in km/s/Mpc)? km/s/MpcWhat is the Hubble time (in yr)? yearsHow old (in yr) would the universe be, assuming space-time is flat and the expansion of the universe has not been accelerating? How would acceleration change your answer?A.If the expansion of the Universe has been accelerating, the Universe could be substantially younger than the value entered above.BIf the expansion of the Universe has been accelerating, the Universe could be substantially older than the value entered above. **Educational Content: Understanding the Hubble Constant and Age of the Universe****Problem Statement:**If a galaxy is 9.0 Mpc away from Earth and recedes at 488 km/s, what is \( H_0 \) (in km/s/Mpc)?**Input Box**: - _____ km/s/Mpc**Follow-up Calculation:**What is the Hubble time (in yr)?**Input Box**:- _____ years**Age of the Universe:**How old (in yr) would the universe be, assuming space-time is flat and the expansion of the universe has not been accelerating?**Input Box**:- _____ years**Considerations on Acceleration:**How would acceleration change your answer? - ○ If the expansion of the Universe has been accelerating, the Universe could be substantially **younger** than the value entered above. - ○ If the expansion of the Universe has been accelerating, the Universe could be substantially **older** than the value entered above.**Need Help?** - Read it**Submit Answer Button**: This content is designed to guide students through calculations relevant to cosmology, involving the Hubble constant and the implications of an accelerating universe on cosmological time scales.

The question above has been given from Hubble's law. This law is also known as the Hubble-Lemaitre Law. This law states that the galaxies are moving away from the earth with such a velocity which is proportional to the distance between them. If v is the velocity with which a galaxy moves away from the earth and D is the proper distance between them which changes with time then v∝D Now to introduce a = sign we have to introduce a proportionality constant known as the Hubble constant H0. Then v=H0D If v has a dimension of LT-1 and D has a dimension of L then H0 carries a dimension of T-1. The Hubble time is the time required by the Universe to expand to its current size if the Universe is not accelerating. It is defined by the reciprocal of the Hubble constant H0. It is given by tH=1H0 Distance from the galaxy to the earth D=9 Mpc The velocity of the galaxy v=488 km/s Now we know that H0=vD=4889km/s/Mpc=54.22 km/s/Mpc If we want to convert Mpc to km then we have to multiply by 3.086×1019. Then D=9×3.086×1019 km Therefore Hubble constant in s-1 is H0=4889×3.086×1019s-1=1.757×10-18s-1 The Hubble time is given by tH=11.757×10-18s=5.691×1017s=18,042,871,638.762 years For flat spacetime and and non accelerating Universe, the age of the universe is the Hubble time =18,042,871,638.762 years If the Universe had been accelerating, then the age of the universe is less than the above age, that is, the universe had been young. Answer: The Hubble constant H0 =54.22 km/s/Mpc The Hubble time tH=18,042,871,638.762 years For flat spacetime and non accelerating universe, the age is =18,042,871,638.762 years If the Universe had been accelerating, it would have been younger than the above age.

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If a galaxy is 9.0 Mpc away from Earth and recedes at 488 km/s, what is H0 (in km/s/Mpc)? km/s/Mpc What is the Hubble time (in yr)? years How old (in yr) would the universe be, assuming space-time is flat and the expansion of the universe has not been accelerating? How would acceleration change your answer? A.If the expansion of the Universe has been accelerating, the Universe could be substantially younger than the value entered above. BIf the expansion of the Universe has been accelerating, the Universe could be substantially older than the value entered above.

If a galaxy is 9.0 Mpc away from Earth and recedes at 488 km/s, what is H0 (in km/s/Mpc)? km/s/Mpc What is the Hubble time (in yr)? years How old (in yr) would the universe be, assuming space-time is flat and the expansion of the universe has not been accelerating? How would acceleration change your answer? A.If the expansion of the Universe has been accelerating, the Universe could be substantially younger than the value entered above. BIf the expansion of the Universe has been accelerating, the Universe could be substantially older than the value entered above.