Let's say a spaceship is approaching Sagittarius A*. How close to this black hole must the spaceship get to experience time 9 times slowly?

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Let's say a spaceship is approaching Sagittarius A*. How close to this black hole must the spaceship get to experience time 9 times more slowly?
Transcribed Image Text:Let's say a spaceship is approaching Sagittarius A*. How close to this black hole must the spaceship get to experience time 9 times more slowly?
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Step 1

The formula for gravitational time dilation is given by 

t=t01-2GMrc2

here, 

t=time in the gravitationally influenced reference framet0=time in a reference frame an infinite distance from any massM=mass of the object being approachedr=distance from the object being approached

for sagittarius A*, the mass is 

M=4.1 million solar masses=8.26×1036 kg

Given that 

tt0=19

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