esc a) 10 points) Gravitational Time Dilation. The escape velocity from the surface (radius r) of a star or planet of mass M is given by the formula v = (2GM/r). Use this expression to write the time-dilation fraction, At/t, in terms of the ratio of vesc to the speed of light, c. Hint: This is just a simple exercise in substitution. 5.98 x 1024 kg b) (10 points) Extra Lifetime on the Surface of Earth. The Earth has mass MEarth and radius REarth 6.38 x 10 m. What is the fractional time-dilation (At/t) for someone on the Earth's surface? How much longer (At) is a typical lifetime on the surface of Earth, compared to someone in deep space, far away from Earth? Assume a typical human life span of t = 80 years. I

Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter44: Particle Physics And Cosmology
Section: Chapter Questions
Problem 30P
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a) 10 points) Gravitational Time Dilation. The escape velocity from the surface (radius r) of a star or
planet of mass M is given by the formula v = (2GM/r). Use this expression to write the time-dilation
fraction, At/t, in terms of the ratio of vesc to the speed of light, c. Hint: This is just a simple exercise in
substitution.
5.98 x 1024 kg
b) (10 points) Extra Lifetime on the Surface of Earth. The Earth has mass MEarth
and radius REarth 6.38 x 10 m. What is the fractional time-dilation (At/t) for someone on the Earth's
surface? How much longer (At) is a typical lifetime on the surface of Earth, compared to someone in deep
space, far away from Earth? Assume a typical human life span of t = 80 years.
I
Transcribed Image Text:esc a) 10 points) Gravitational Time Dilation. The escape velocity from the surface (radius r) of a star or planet of mass M is given by the formula v = (2GM/r). Use this expression to write the time-dilation fraction, At/t, in terms of the ratio of vesc to the speed of light, c. Hint: This is just a simple exercise in substitution. 5.98 x 1024 kg b) (10 points) Extra Lifetime on the Surface of Earth. The Earth has mass MEarth and radius REarth 6.38 x 10 m. What is the fractional time-dilation (At/t) for someone on the Earth's surface? How much longer (At) is a typical lifetime on the surface of Earth, compared to someone in deep space, far away from Earth? Assume a typical human life span of t = 80 years. I
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